Mutilation Interrogation

The heroine is strapped to a chair. She's told to talk by the villain. If she doesn't, the henchman standing beside her will start cutting her fingers off. One by one. If she's not talking by then, he'll move onto other areas.

One of the many forms of Cold-Blooded Torture or the Jack Bauer Interrogation Technique. See also Fingore and Kneecapping, which this tends to include.

No real life examples, please; All The Tropes does not care to squick its readers.

Examples of Mutilation Interrogation include:

Anime, Manga, and Light Novels

Claire from Baccano!! does this to one of Ladd Russo's men, Dune. Of course, Claire being the master of overkill that he is, doesn't simply cut off digits, but rather pulls him under a moving train and slowly grinds his arm off on the rails until he starts talking.
- Claire likes doing this in general—hence the horrific condition of the corpses left behind by the Flying Pussyfoot. And when one of his victims claims that he's been through enough torture to be immune to it, Claire informs him that he can do far worse yet.
Weiss Kreuz. In one of the drama CDs, Birman is interrogated this way - by the time Weiss manages to rescue her, she only had enough fingers to pick up a gun and shoot herself.

Comic Books

Eric Draven does this to a bad guy in The Crow graphic novel to get him to talk: "It took three fingers, but he talked."
In Elf Quest, Ekuar reveals that the troll King Guttlekraw would torture his elven prisoners by amputating fingers, then limbs. As proof of this, Ekuar himself has only one arm (with a finger missing), and a wooden leg.
In The Punisher story-arc Up Is Down and Black Is White, Frank and some friends have Smug Snake Rawlins tied up in a motel room and are trying to think of how to get him to talk. Frank is left alone with him and...

O'Brien: What'd you do to Rawlins?
Frank Castle: Took an eye out of him.
O'Brien: ...well, why fuck around when you don't have to.

- There's also the scene in the film The Punisher in which Castle chains up a man in his room and proceeds to go into a lengthy explanation about how torture via blowtorch basically has you smelling your own flesh cooking before feeling cold from the nerve endings being fried, before letting the soon-to-be tortured man catch a glimpse of a blowtorch and letting him have it. Subverted ultimately because Castle never did blowtorch the guy. He only cooked a slab of meat (hence the "smell your own flesh cooking" bit) and poked the man in the back with a Popsicle. The result was that the man thought he was being burned to death and spilled his guts only to be released unharmed.
- In The Slavers, The Punisher is tracking down the leaders of a Human Trafficking ring. When he gets one of the three bosses, he knocks the man out, drags him out to the woods, and cuts him open, pulling out the man's intestines. Then he wakes the man up and starts asking questions...
Black Mask likes to use this trope, drills, irons (as in ironing irons, with the steam and the hurting and the OH GLAYVEN. His ... interrogation partners end up looking a whole less pretty than they used to be..
When King Mob is being tortured by Sir Giles in The Invisibles, he has his fingers dropped in his lab after a convenient blackout. Subverted in that he's merely been injected with an experimental drug that allows him to perceive written language as a tangible object—e.g., he's given a slip of paper reading "Your Severed Fingers," and sees his severed fingers.
Rorschach takes this trope and runs with it. He goes to a bar where he believes he can get some information, grabs a random person, and then asks the rest of the bar for the answers. Getting no response, he breaks one of his fingers, then asks again. Next shot, he's walking out of the bar, having recieved no information. We never hear what happened to the guy.
This happened to Luca from The Meek, and as a result his fingers still don't work right, years later. As he put it, "It took them seven fingers to figure out that I didn't know anything."
The Hellblazer arc Son of Man has Mob torturer Gestapo threaten a target with nothing more than a pair of nail clippers. We later find out what they were used on: his eyelids.

Fan Works

Happens in the Artemis Fowl fanfic "Within Temptation".
It doesn't actually involve amputation, but in Backwards Compatible by Ruskbyte, Harry interrogates Malfoy about Hermione's disappearance by breaking his fingers one-by-one. In the Great Hall.

Film

James Bond in Live and Let Die.
Quentin Tarantino's Reservoir Dogs has Mr. White mentioning this to his protege who (unbeknownst to him) is a cop:

"If you wanna know something and he won't tell you, cut off one of his fingers. The little one. Then tell him his thumb's next. After that he'll tell ya if he wears ladies underwear. I'm hungry. Let's get a taco."

Chevy Chase's character in Spies Like Us was threatened with this one after being captured by Soviets. Only through Obfuscating Stupidity (or actual stupidity) was he able to stall long enough to keep his digits:

Soviet Agent: For every question you do not answer, I cut off a finger...
Fitz-Hume: Mine, or yours?

This happens to Mel Gibson's character in Payback. He kidnaps the son of the most powerful mob boss in the city, so they politely ask him for the location using his toes and a hammer.
In the movie Man On Fire, Denzel Washington actually tapes the guy's hands to the steering wheel and takes a few fingers off. Then he blows the car up or something.
- Oh, it's worse than that. He cuts off the man's fingers one by one, slowly, and then cauterizes the wound with the car's cigarette lighter immediately. Then he gives the guy a smoke and pushes the car off a cliff (though at that point the guy was just glad it was over).
- Denzel's character uses this trope several times in the movie, including blowing off a man's fingers with a shotgun.
Played for laughs in Shrek when the Gingerbread Man gets both of his legs broken of and his head dipped into a glass with milk. Lord Farquaad then crushes one of the legs in his hands, but the other leg is later reattached with frosting, making it neccessary for Gingy to walk with a candy cane.
In the film noir/lesbian romance Bound, a mobster steals a couple of million dollars from his employers. Despite a savage beating, he refuses to tell them where he's hidden it. Then one of the mobsters produces pruning shears, holds the guy's hands over a toilet bowl, and says: "I'm going to ask you ten times."
"I'm gonna ask you questions. And every time you don't give me answers...I'm gonna cut something off. And I promise you, they will be things you will miss." No mistake about it, Beatrix Kiddo does not fuck around. And the very first part that she starts with is Sofie's other arm, as she already chopped off the other one...
- The Japanese cut has her making good on this threat.
Quoth Durant from Darkman after taking out a cigar cutter. "Now, let's consider my points, one by one. One. I try not to let my anger get the better of me. cut "Two. I don't always succeed." cut "Three. I have seven more points."
Happens in Battle Beyond the Stars, though it could have just been because the Big Bad wanted a new hand.
In Blue Thunder, Lymangood is kidnapped and threatened with having his fingers broken, one by one, until he reveals the location of the tape exposing the Government Conspiracy. Surprisingly for a character who had, until that point, been the Plucky Comic Relief, he feigns acquiescence and then makes an escape.
Played horrifically straight in the French film Les femmes de l'ombre, involving some Nazis and one of the eponymous femmes, who is a member of La Résistance.
Marathon Man. Two words: Nazi dentist.
In Oldboy, the protagonist Oh Dae-su tracks down the illegal holding facility where he was kept for 15 years after being kidnapped off the streets. Dae-su asks the warden who paid him to hold him, and when the warden doesn't answer he duct tapes him to his chair. He then uses his claw hammer to pry out the man's teeth one at a time, telling him that he owes him one tooth for each year of his life that was stolen from him. After about 7 or so, he gives the warden a chance to talk, with the implication that he'll continue through with all 15 if he doesn't.
Near the end of Body of Lies, the protagonist is tortured by repeated smashing of his fingers with a hammer. It is later implied that he lost at least parts of one finger in the process.
In The Tourist, the Big Bad threatens Angelina Jolie's character with this after she is captured.

Literature

Martian Deathtrap, a novelization based on the Mars Attacks! comics/card series by Topps, has the Martians capture a showgirl and using a surgical tool that cuts and cauterizes at the same time on the bottoms of her toes after she refuses to tell them (a) how many humans are still alive in the mansion they're all trapped in and (b) how to drive a car, of all things. Given they could have just forced her to take them to the cars and have her drive them to safety at gunpoint, the torture might have been a bit excessive, if not totally unnecessary.
This trope happens in one of the later Anita Blake books, where Anita threatens to cut the fingers off of a henchman when he doesn't tell her where Richard's mother and brother are. He loses one finger before he talks.
Another inversion in The High King's Tomb, third book in the Green Rider series. In this one, a female interrogator does this to an evil henchman who had already lost one hand. To top it off, this same henchman had driven the interrogator's brother to suicide by blaming him for an incident that made their sadistic master cut off both hands.
This happens to Tia, a major character of Jennifer Fallon's Second Son's trilogy. This is more of a warm up for the torture that would have occurred however. Years later the protagonist asks her if she has any idea what her enemy would do to her and she replies that she has a pretty good idea, holding up her mangled fingers for emphasis. The protagonist, Dirk, swiftly explains that she has no idea whatsoever, having being made privy to some of the real methods that the Torture Technician employs (he was very happy to explain it to someone who he thought would be able to appreciate how cleverly brutal and twisted, and effective, it could be. The protagonist Dirk had to pretend to find it fascinating).
In the Stephanie Plum novels, the main character was threatened with this on at least one occasion. There was a slight subversion in the latest novel, where the villain was trying to motivate her to do something for him by mailing her someone else's fingers.
- She's actually sent dismembered body parts or finds them in her fridge in more than half the books, but that usually isn't an interrogation method as much as it the psycho of the book trying to warn her to back off or get her attention. (Memorable instances include a giant mole and a dismembered penis. The penis made her grandmother nostalgic.)
Multiply inverted in Dean Koontz' novel Sole Survivor; agents of a secret conspiracy threaten to do this to a flight controller's son if she doesn't keep quiet about what she heard on a black-box recording. Worse, her son will be told that she could save him by cooperating, but in fact they'll keep cutting regardless of what she does, once they've started.
Happens to the cop protagonist in the book/film Sharky's Machine. Every hour they cut off part of his finger at the joint. I think he loses a complete finger before he escapes.
This turns out to be the reason Vlad Taltos is missing a finger in the later books: he got caught by a Torture Technician in Jhegaala.
Inflicting this is the job of Glotka in Joe Abercrombie's The First Law books.
In Tom Clancy's novel The Sum of All Fears, the Arab terrorists who set off a nuclear bomb in Denver have their fingers broken one by one by John Clark until they reveal their sponsor (specifically, he muses later that he didn't have to break all their fingers, and that what mattered more was how you worked the broken digits). Of course, it turns out that they're lying in an attempt to provoke all out warfare with the Arab world, but the goodguys figure this out in time to avoid a catastrophe.
Neverwhere: Mr Vandemar breaks Richard's finger and is about to cut off his ear when Door gives in and agrees to open the door to Heaven. She's lying, though.
In Don Pendletons The Executioner series of books, the mafia have interrogators that turn people into "Turkeys" by taking several days to slowly carve them up. The first two cuts are to remove the eyelids.
In the Lensmen books, when Jill is captured, she is threatened with this. Her brave defiance is Honor Before Reason because she managed to alert the Lensmen who are in telepathic contact with her and urging her to talk because they can ensure that no one who hears will get out alive.
The principal viewpoint character of The Zoo Gang by Paul Gallico has no fingernails because the Gestapo pulled them out approximately twenty-five years before the events of the book. That the rest of his group are still alive indicates he didn't talk.
Lawrence Block's insomniac thief, Evan Tanner, does this ot one of the baddies in Tanner's Virgin (originally published as Here Comes a Hero).

Live Action Television

Happens to Sydney Bristow in the pilot episode Truth Be Told - with teeth. She ends up losing her number 5 right molar (not a visible tooth usually, because Beauty Is Never Tarnished).
Gender Flipped by Lost: Ana-Lucia threatens to cut off Nathan's finger unless he confesses to being an Other. However, this threat causes the real Other to kill Nathan and make it look like he got away.
Octavian and Pullo use this method on Evander in Rome to get him to fess up about having had an affair with Niobe.
Jayne threatens mole Dobson with this in order to find out how much the Alliance knows from the transmission he sent. A spooked Dobson immediately blurts that the Alliance knows everything, leading a disappointed Jayne to deduce that they know nothing. "Was gonna get me an ear, too."
Blakes Seven: Blake suspects (correctly) that the surgeon who's repairing Gan's malfunctioning Morality Chip is delaying the surgery long enough for the Federation to catch up with them. Blake tells him that if the operation isn't finished by a certain time, he'll destroy his hands; a very apt threat for a surgeon.
In the TV adaptation of Casino Royale 1954 in Climax!, the ball-whacking is substituted out for Bond's toenails being painfully pulled out.

Video Games

Armed and Dangerous started with the torture by cutting out the tongue and proceeding from there.

Web Comics

Last Res0rt - The first time we see her, Daisy Archanis is missing HER LEFT LEG from mid-thigh on down, and Veled apparently had something to do with it...