I Will Tear Your Arms Off

A specific form of Cut His Heart Out with a Spoon in which a character is so consumed by rage that he threatens to rip someone's limbs off with his bare hands. The delivery of the line tends to be either Large Ham or Dramatic Deadpan, depending on the character.

The threat is very rarely carried out, at least on screen. If the character is actually capable of this kind of violence, he may mention having once done this as a casual aside. If it is carried out and the victim is a recurring character, he will usually get better. May overlap with Comedic Sociopathy and Bloody Hilarious.

Examples of I Will Tear Your Arms Off include:

Comic Books

Happens frequently do Doctor Octopus. Usually goes like this:

Super Hero: I hope you're ready to lose those arms.
Ock: Insolent fool! My tentacles are constructed with [whatever 'indestructible' metal he's building his arms with this month] plating! You could not even hope to scratch them!
Super Hero: I wasn't talking about the metal ones.

Film

During the song "I Wanna Be Like You" from The Jungle Book, when Baloo and Bagheera are trying to rescue Mowgli from King Louie and the apes, Baloo actually tells himself, "I'm gonna tear him limb to limb..."
In How to Train Your Dragon, when Gobber tells the recruits that he lost his leg and hand to a dragon, Snotlout says, "I'll avenge your beautiful hand. And your beautiful foot. I'll cut the legs off every dragon I see. With my face."
The Princess Bride: Inigo and Fezzik need to get into a castle.

Westley: Give us the gate key.
Yellin: I have no gate key.
Inigo: Fezzik, tear his arms off.
Yellin: Oh, you mean this gate key [pulls it out].

In Star Wars, Chewbacca wails, Han Solo translates.

Chewbacca: Aaaaaaaaaaaaaaaarrrgh!
Threepio: He made a fair move. Screaming about it can't help you.
Han Solo: Let him have it. It's not wise to upset a Wookiee.
Threepio: But sir, nobody worries about upsetting a droid.
Han Solo: That's 'cause droids don't pull people's arms out of their sockets when they lose. Wookiees are known to do that.
Chewbacca: Grrf.
Threepio: I see your point, sir. I suggest a new strategy, Artoo: Let the Wookiee win.

Judge Dredd: Rico's ABC robot is holding Judge Hershey by the neck. When Dredd refuses to join Rico's plan to take over the city, Rico threatens to have the robot rip Judge Hershey's arms and legs off.

Literature

Not played for laughs at all in Harry Potter and the Prisoner of Azkaban. Hagrid recounts how he met Sirius Black the night of the Potters' murder, and he says that if he had known his role in their deaths, he'd have torn Sirius limb from limb. Hagrid is a half-giant, so he means it, and can follow up on it.
This trope is made Older Than Print by Beowulf; Beowulf tears Grendel's arm off while locked in a pure test of strength with the monster. He then displays it as a trophy over the door.
Happens a few times in the Redwall series, often followed up with a threat to feed the removed body parts to the victim. On at least one occasion said threat is made by a badger, and they quite easily could follow up on it.

Live-Action TV

"I'll rip your bloody arms off!" was the catch phrase of Aunty Jack of the Australian cult comedy series The Aunty Jack Show.
The Increasingly Poor Decisions of Todd Margaret: "Give me my money, or I will rip off your arm and stuff it down your cock-hole."
"And Crilly if you try to bullshit me like that again, I will rip off your arms."

Video Games

Done literally in Lego Star Wars 2 by Chewbacca. Given that it is LEGO, it is more humorous than horrific.
Dragon Age: "Sten, tear his arms off."

Web Comics

RA Ruth Lessick has a way of getting dormies to come to the floor meetings....
The reason why Matilda of Dan and Mab's Furry Adventures was exiled.

Web Original

Preston Stormer threatens to do this to the DJ Mak Megahertz in one of the Hero Factory podcasts. It's implied that he carried out the threat, too, but Mak's a robot, so he gets repaired.

Western Animation

SpongeBob SquarePants: Man Ray threatens to do this to SpongeBob if the latter doesn't release him. Later in the episode as he tries to pass as a reformed villain, he makes the same threat to Patrick when the latter's stupidity made the task of returning a wallet to him like a good person impossible to accomplish.
In the Ren and Stimpy episode "Sven Hoek", this is one of the threats Ren gives Stimpy and Sven for messing up the house.
One episode of Regular Show had Rigby and Mordecai scribble various complicated mathematical equations all over the kitchen counter as a result of them being hallucinated by Benson's "special drink", and when Benson finds out all about this, he scolds the two into erasing all the "graffiti" on the counter or else he will tear their limbs off.

Real Life

"I'll rip your legs out of your ass!" is a common saying/threat in Poland.