1
general::
Talk incessantly, babble, as in Wilbur is always running off at the mouth about his investments. This idiom transfers a flow of water to an unending flow of words. [Slang; c. 1900]
American Heritage Idioms
2
general::
Phrase(s): run off at the mouth
Sl. to talk too much. • I wish you would stop running off at the mouth. • Tom runs off at the mouth too much. I wish he would temper his remarks.
McGrawhill's American Idioms And Phrasal Verbs