The punch is like a needle, only bigger. It's essentially a tube with one end sharpened. Doc twirls it on tissue to cut it in, removes tool, grabs tissue cylinder with forceps, pulls and cuts. Sounds worse than it is -- Local anesthesia, of course.
Here's a photo of a set of various sizes from 1.5 to 8mm (Hmm, that one's a bullet hole of 31 Caliber!), mine was 3mm:
http://www.claflinequip.com/ProductDetail/zoom.asp?img=CESS-5911-00.jpgAlso, I think the needles come in much longer lengths, like for kidney biopsy.