1. To do something in order to keep someone from speaking about something, especially a secret or damaging piece of information. The company tried to bribe me with a cash payout in order to shut my mouth, but there was nothing that would stop me from talking about the illegal things I'd seen while working there. We've got to find a way to shut her mouth; her testimony could bring down our entire organization.

2. To choose not to speak, especially to be tactful, to keep a secret, or to stop irritating someone. I could tell my encouragement wasn't helping, so I just shut my mouth. I'm going to shut my mouth before I say something I'm not supposed to! Tim, if you don't shut your mouth, I'm going to come over there and shut it for you.