These sound odd to me, but: My shoe got cut. I got a cut in my shoe. (And since this will be obvious to anyone looking at my shoe, I would probably tell the person exactly how it happened so that it made sense: "My foot slipped under the back of the lawn mower and the blade sliced through the top of my shoe. Lucky I didn't lose a toe.")
Keep in mind with all of these that you're either talking about one shoe or both shoes, and be sure to use the right one for your shoe problem.