Ditto on using a drill press unless the piece you're cutting a plug out of is very securely fastened down onto a scrap piece and then onto a table AND you're using a powerful variable speed drill/driver. Clamps are recommended because if/when you first touch the cutter to the wood, it will want to spin the piece of unsecured wood. Also, if you're using a handheld drill, go slow enough so that it doesn't walk about or bog down in the wood but not so fast that if the cutter binds or hits a defect and stops, the drill doesn't snap your wrist or fly out of your hands. And, never, ever bear down with your weight on the cutter.
EDIT: Shame on me! I neglected to mention that you must be sure to keep the plug cutter as straight as is possible as you drill with it so that it doesn't cant and snap or chew up the plug or jam and kick back in the piece of wood.