When using a leather punch, I've found that the little cut-out circles of leather build up inside the tips. If you don't clean out the tips, the punch will no longer be able to make a clean cut. Instead, you'll end up compressing leather instead of cutting it.To clean the tip of a leather punch, I place a thumb tack pointy-side-up on the hard surface where you would typically put the leather you're cutting, and I drive the punch down onto the tack. Ideally, the tack will skewer the leather build-up, and when you lift the punch away, you'll have a little leather-kabob on the tack. Scrape the leather off the tack and discard it.

If the tack jams the build-up of leather further into the tip of the punch, you should be able to remove the tip and tap it on something to get the build-up to drop out. My punch has five swappable screw-in tips, so I just unscrew the tip and force the leather out the back of the tip. If you have a rotary punch, check to see if the tips are removable. If they aren't, you probably need a different punch!