Mangled Catchphrase

Smithers: Sir, the actors are here to audition for the part of you.
Mr. Burns: Excellent.
Anthony Hopkins: Excellent... hisssss!
Mr. Burns: Next!
William Shatner: Exc! Ell! Ent!
Mr. Burns: Next!
Bumblebee Man: Excelliente!
Mr. Burns: Next!
Homer: Exactly! .... D'oh!

—"A Star Is Burns", The Simpsons

If there's one thing that imposters, imitators, and other depictions of characters in media can never get right, it's the Catch Phrase. No amount of research ever seems to counteract this; nor does the relationship between the characters involved.

When other characters can't recognize an imposter in spite of the Mangled Catchphrase (or other details), see Easy Impersonation. Conversely, when the characters around know the imitated well and aren't holding the Idiot Ball, this can be a convenient way to Spot the Imposter. When they get it right, see Borrowed Catchphrase.

Examples of Mangled Catchphrase include:

Anime

In the first Ditto-centric episode of the Pokémon anime, Ash and his friends dress up as Team Rocket. To Rocket's frustration, they can't correctly recite Team Rocket's motto.

It's "unite all peoples within our nation", not "ignite"!

Literature

In Discworld, Cut-me-own-Throat Dibbler manages to mangle his own catch phrase after Vimes travels 33 years into the past and inadvertently teaches it to him.

Live Action TV

In Red Dwarf, Rimmer renders Ace's "Smoke me a kipper, I'll be back for breakfast" catchphrase as "Stoke me a clipper, I'll be back for Christmas".
In the Doctor Who episode "The Almost People", the Doctor takes this Up to Eleven by managing to mangle two of his own catch phrases at once. It Makes Sense in Context.

I reversed the jelly baby of the neutron flow!

Video Games

In Final Fantasy VII, several main characters attempt to pre-empt Barret's catch phrase, "There ain't no getting offa this train we're on." One character renders it "The train we're on don't make no stops!"
In Final Fantasy Tactics A2, pseudo-Vaan attempts to invoke Vaan's use of the phrase "the leading man" (which he, in turn, picked up from Balthier sans mangling). However, Vaan and Balthier simply passively refer to the "leading man" in the third person, generally not stating who the leading man is or what he leads. Pseudo-Vaan...

"Vaan": Nay, 'tis I, Vaan!... 'Twere this a play, I'd be leading man!
Luso: If this is a play, the acting's terrible.

In Tales of Monkey Island, Stan attempts to sell Guybrush dolls that can't quite get the "three-headed monkey" line down.

Doll: That is the second-largest monkey head I have ever observed!

Web Animation

When Homestar Runner realizes he just broke up with Marzipan over a complete misunderstanding on his part alone over her answering machine, he rushes to Marzipan's house and replaces the tape with a tape of Homestar himself badly imitating several characters. He tries, and fails, to say "job" incorrectly like Coach Z does several times.
- Also in the 50th Strong Bad Email, when Strong Bad gets a phone call, distracting him from his goal of answering 50 emails in a row, and Homestar attempts to answer the emails like Strong Bad:

Homestar: "Dear Strong Bad, how do you type with gloves on your hands?" Oh, even I know what to do with this one. BALEETED! Wha--? Oh. Umm... DELTEATED! No? Uhh... Del Taco?

- Also the Bonus Email "Comic Book Movie".

Strong Bad: "Let's hear your best "Stiny, get me a danish!""
Crack Stuntman: "Shiny, throw me that donut!"

Web Comics

This one was probably deliberate, but the Monkeyspank virus of Captain SNES came up with his own vision of retooling the comic to avoid copyright violations, ending with the catch phrase "Honeyed Kwanzaa, it's idiotically new!", twisting Alex's usual "Sweet Christmas, that's stupid fresh!"

Western Animation

In one episode of Buzz Lightyear of Star Command, Buzz ends up in what he believes to be the future, complete with a statue of himself that says "To infinity and even further!"
You think he'd know better, but Brain of Pinky and The Brain tries to trick the Earth, recently brought to life and angry with Brain (long story), by pretending to be Pinky. He spouts several of Pinky's Verbal Tics... but accidentally slips in a word Pinky does not say, which is what reveals him as an impostor.
In The Simpsons episode "A Star is Burns", Burns holds auditions for an actor to play him in an upcoming movie. No one can correctly render his trademark "Excellent", but Homer gets it worst of all: "Exactly. Heh heh...D'OH!"
- In another episode, Mr. Burns hires Michael Caine to impersonate Homer. Homer's usual "D'oh!" is instead said as "B'oh!"
- And when Rainier Wolfcastle attempts to play Radioactive Man, he turns the latter's "Up and atom!" into "Up and at them!"
- In "Goo Goo Gai Pan", a spy impersonating Bart gets his catchphrases wrong, saying "Don't have a cattle, dude!" and "Feast on my shorts stupid father man!"
In The Spectacular Spider-Man, Chameleon says, when imitating the hero, "My insect early warning sense is vibrating!"
In the Scooby Doo Mystery Inc episode "Howl Of The Fright Hound," Scooby is accused of attacks made by a robot Great Dane and is locked up in an animal asylum. Shaggy is left miserable, and Velma tries to cheer him up with a "Relma Delma Doo!" that everyone thought was incredibly lame.
Atom Ant mangles his own catch phrase "Up and at 'em, Atom Ant" in an episode where he's tempted with a picnic. Instead he says "Up and eat 'em, Picnic Ant!"