Wikipedia: Breaking character
In theatre (especially in the illusionistic Western tradition), breaking character occurs when an actor ceases to maintain the illusion that they are identical with the character they are portraying. This is a more acceptable occurrence while in the process of rehearsal but is considered unprofessional while actively performing in front of an audience or camera (except when the act is a deliberate breaking of the fourth wall). One of the most common ways of breaking character is corpsing, in which an actor loses their composure and laughs or giggles in a comedy scene or scene requiring ludicrous actions. If the breaking of character is particularly serious, it would normally result in an abandonment of a take in recorded or filmed drama.
 
(Oxford English Dictionary)
corpse, v.
Actors’ slang. To confuse or ‘put out’ (an actor) in the performance of his part; to spoil (a scene or piece of acting) by some blunder.
1859   J. C. Hotten Dict. Slang 24   Corpse, to confuse or put out the actors by making a mistake.
1886   Cornhill Mag. Oct. 436 (Farmer)  He [an actor] expressed a hope that Miss Tudor ‘wouldn’t corpse his business’ over the forge-door again that evening.
intransitive. Of an actor: to forget one’s lines; = dry v. 2d; to spoil one’s performance by being confused or made to laugh by one’s colleagues.
1874   Hotten’s Slang Dict. (rev. ed.) 129   Corpse, to stick fast in the dialogue.
1958   News Chron. 23 May 4/7   There’s a new word, too, from drama school. When anyone forgot their lines in the past they had dried. Today, they have ‘corpsed’.
       
Google Books 
Newspapers.com
Dickens Journals Online
October 1853, Household Words (a weekly journal conducted by Charles Dickens), “Slang,” pg. 77, col. 1:
And the Stage has its slang, both before and behind the curtain. Actors speak of such and such a farce being a “screamer,” and such and such a tragedy being “damned” or “goosed.” If an actor forgets his part while on the stage, he is said to “stick ” and to “corpse ” the actors who may be performing with him, by putting them out in their parts. A “part” has so many “lengths;” a piece will “run ” so many nights. Belville is going in the country to “star ” it. When no salaries are forthcoming on Saturday, the “ghost doesn’t walk”—a benefit is a “ben,” a salary a “sal;” an actor is not engaged to play tragedy or comedy, but to “do the heavy business,” or “second low comedy,” and when he is out of an engagement he is said to be “out of collar.”
 
Newspapers.com
2 February 1878, Buffalo (NY) Express, “The Dramatic Man” by Vlen-Ten, pg. 3, col. 4:
We became initiated in the business to the degree that we readily comprehended the difference between a “gooser” and a “screamer,” and grew ashemd of our horror on hearing for the first time of the mysterious and rather alarming practices of “mugging up” and “corpsing.”
 
Google Books
A Dictionary of Slang, Jargon & Cant
By Albert Barrère and Charles Godfrey Leland
London: George Bell & Sons
1897
Pg. 260:
Corpser. Vide To CORPSE.
Corpse, to (theatrical), to confuse, to put out fellow-actors by sticking fast in the dialogue; kill a scene through ignorance, willfulness, or stupidity. A contretemps of this kind is called “a regular corpser.”
 
A Glossary of Theatre Terms
copyright, Peter D. Lathan 1996-1999
(...)
Corpse
Not a dead body in a thriller! An actor who gets an unintended and uncontrollable fit of laughter on stage is said to “corpse”.
   
21 June 2008, Edmonton (Alberta) Journal, “This is the season that was ...; Distinctly dark, comically macabre, full of corpses and ghosts and prompting the question” by Liz Nicholls,, pg. C1:
EDMONTON - Will 2007-08 on Edmonton stages be remembered as the season that the theatre slang “corpsing”—breaking out of character to giggle uncontrollably—took on a new and literal meaning?
     
Twitter
Brian J. Smith
@BrianJacobSmith
Oh, sorry - “corpser” is an old stage term for someone who easily laughs in the middle of scenes, usually at the highjinks of other actors.
1:49 PM · Sep 6, 2009
 
Twitter
katie ﻬ
@ivegotcake
Kaz and myself are terrible corpsers. When she joined the show, Karen never corpsed at all. As time went by I found ways of making her laugh
11:44 AM · Jan 13, 2013
 
YouTube
Lin-Manuel Miranda Teaches You Broadway Slang | Vanity Fair
Vanity Fair
Nov 27, 2018
Vanity Fair cover star Lin-Manuel Miranda teaches you Broadway slang.
   
Vanity Fair
SLANG SCHOOL | SEASON 1 | EPISODE 35
Lin-Manuel Miranda Teaches You Broadway Slang
Vanity Fair cover star Lin-Manuel Miranda teaches you Broadway slang.
Released on 11/27/2018
Transcript
(...)
Corpse.
You know, I’m realizing how many ghoulish
and macabre theater terms there are,
and none is better than corpse,
which basically means to crack up on stage.
It’s also part of what makes theater great.
It’s what reminds you you’re not at the movies.
   
22 April 2021, Daily Express (London, UK), “Lockdown saved me from a breakdown” by Jane Oddy, pg. 22:
“It was enormous fun as Razor Ruddock is really hilarious. He was flirting with me and trying to make me grin. I like it when people try and make me laugh. I think of myself as a terrible corpser [theatre slang for someone who laughs uncontrollably]. I’m amazed I don’t corpse more often,” says Anne.
 
Twitter
Balfe Nation
@balfenation
On #Outlander and #SamHeughan’s insta today:
“Proof! #CaitríonaBalfe is a brilliant costar and terrible corpser! We’ve had a great year with plenty of laughs, can’t wait to show you Season 7🙌
3:40 PM · Dec 9, 2022