A cut or curtailed dog. According to the forest laws, a man who had no right to the privilege of the chase, was obliged to cut or law his dog: among other modes of disabling him from disturbing the game, one was by depriving him of his tail: a dog so cut was called a cut or curtailed dog, and by contraction a cur. A cur is figuratively used to signify a surly fellow.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
cupid * curbing lawNathan Bailey's 1721 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes