I use a classic leather punch with the rotating head which gives you different size holes. I use a lot of snaps and it has cut a clean hole in all types of fabric.
You could sandwich your bit between 2 bits of cotton fabric to be sure of a clean cut.
ETA
I've just realised that you said 12 - 14mm holes. If I was doing that I would make the biggest hole I could with the punch then enlarge it with small, sharp, pointed scissors. I did that for eyelets on a canvas bag and it worked just fine.