Cur A fawning, mean-spirited fellow, a crop-tailed dog (Latin, curtus, crop-tailed. French, court; our
curt). According to forest laws, a man who had no right to the privilege of the chase was obliged to cut
off the tail of his dog. Hence, a degenerate dog or man is called a cur.

My dictionary gives no etymology for "curmudgeon" . The one above makes sense to me.
I have seen the word "curtal" applied to peasants' dogs that had been mutilated.