"Ass" is a complicated word for an English language learner.
In the UK it's ARSE an Ass is like a donkey
Ass is not like a donkey. It IS a donkey. "Dumb-ass" as in "dumb donkey" not "dumb butt".
EDIT: I could be wrong, though. It could be "dumb arse". ;S
It's definitely dumb-arse. A perfect example of British swearing can be found watching the Royle Family.