It depends on if it's a fully domestic cat or one that has spent significant time living on it's own in the wild (stray/feral).

I've seen a domestic cat play with a mouse until it's dead, then act like it doesn't know what to do with it. An old stray cat (that had rejoined domestic life but didn't have the energy to catch and play with the mouse) would then get up and eat it in two chomps.