Mouth is where some say river begins (5)
I believe the answer is:
sauce
'mouth' is the definition.
(both can mean insolence or rudeness)
I don't understand how the rest of the clue works.
(Other definitions for sauce that I've seen before include "Dressing served with food" , "Relish or impertinence" , "Liquid on food" , "Accompaniment to meat ect" , "Meat dressing" .)