A punch cutter cores the cap. The cigar stays closed around a hole, which some smokers find tidier and others find too tight, especially on a small ring gauge. It is a poor match for a pointed figurado unless the punch is tiny and the head is blunt enough to sit on.
Keep the barrel clean. A packed punch is a plugged cigar waiting to happen. It will not fix a bunch that was tight to begin with; that is a draw problem from the rolling table.
Part of the cutter family, next to guillotine and v cut.