to keep on talking on a subject that is causing distress to others and provoking a fight
If you keep running your mouth, you are going to cause a big fight!
talking shit, stirring shit, letting your mouth run off without thinking.
"Stop running your mouth like a bitch!"
"Dave has been running his mouth about me to everyone."
"ZOMG STFU NUBBIE DNT RUN YUR MOUF AT MEH!!1!11111"
saying smart ass things and generally bitching at a fast pace. Yelling out paragraphs of bitchyness really quickly. Blabbing nonsensical things in an argument just to take up time and have your voice heard.
(the running part means that is is done at a fast pace or else it would be called "walking your mouth")
"they were in a rational argument and she said something that offended him, so he started running his mouth to show his disaproval"
Him: hey, Jessica
Her: My name isn't fucking Jessica
Him: fuck, fuck, fuck, man, fuck, just fuck it man, fuck, fuck, fuck
Her: What the hell is wrong with you!?
Him: you need to stop running your mouth.
Her: Uh, I'm pretty sure it's you who is running their mouth.