From mouth + off.
mouth off (third-person singular simple present mouths off, present participle mouthing off, simple past and past participle mouthed off)
- (intransitive, slang) To complain or otherwise express oneself in a loud, immoderate manner.
- (transitive, intransitive, slang) To talk impudently, especially to one's superior.
2008, Herbert, “Play It Again, Brian”, in Family Guy:
- And don't you mouth off to me, or I'm gonna slap you right in your penis.