Take the tire off. Look at it from the inside. If the cut even goes all the way through, nine times out of ten, the cut is about a millimeter long. Put a little piece of duct tape/gorilla tape/shoe goo over it and remount the tire.

I've had a cut on my rear tire about 2x the size of the one pictured, and it's been there for nearly 2,000 miles. Because on the inside of the tire, it's almost imperceptible. If the cords are damaged, the cut will keep spreading and you won't be able to stop it.