Mice traps are horrible indeed. We had mice in our house soon after moving in and I set a few traps each night, despite not liking the idea. One night, one went off not long after tucking myself in to bed for the night. I had to get up and go downstairs to investigate, and the sight I was confronted with was rather sickening - I had to throw the whole thing away (mouse and trap). It must have been quick though.
Shortly after this we got a rescue cat. She is not particularly a hunter (we have never seen her with a mouse or bird - but she is not let out at night). The mouse problem stopped straight away of course (presumably they sensed our cat and just stuck to other houses in our terrace!).
I bet your cat thought it was clever catching a caught mouse!! :D
