shoot off at the mouth
1. To speak without discretion; to speak too loudly or freely, especially about sensitive topics or information. We would have gotten away with our plan if your dumb cousin hadn't started shooting off at the mouth all over town. I figured it went without saying that I didn't want to talk about my divorce at Daniel's wedding, but you just had to go and shoot off at the mouth like that!
2. To be annoyingly or overbearingly talkative, especially in a bragging or boastful manner. There's some guy at the other end of the bar shooting off at the mouth about how far he can throw a football.