Green’s Dictionary of Slang

mouth v.

1. [mid-19C] (US campus) to bluff a recitation.

2. [mid-19C+] to insult, to criticize, to speak insolently.

3. to hit in the mouth.

4. [1990s+] (W.I.) to make fun of.

In phrases

mouth off (v.) [1950s+] (orig. US)

1. to speak impudently.

2. (also mouth on) to boast, to brag.