
Laugh, scream, etc. your head off
Exaggeration
The phrase uses hyperbole and doesn't mean literally losing one's head.

At the party, we laughed our heads off at the absurd costumes.
Intensity
This phrase emphasizes a very high degree of emotion.

She was screaming her head off when her favorite band came onstage.
Informal
It's casual language, appropriate for friendly conversations, not formal ones.

They were crying their heads off after watching the funny movie.
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