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.
What would you have, you curs, That like nor peace nor war?
Shakespeare: Coriolanus, i. 1.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Cur from Infoplease: