I use pair of wire snip pliers that you can buy at Michael's or Hobby Lobby. The cheaper one with the blue plastic handle. I think that it comes in a pack of 4 or 5 different craft pliers. It's perfect because the angle of the blades are very open, so that you can get under the neck.
My method takes some practice, but once you get a feel for it, you can knock out ten figures in a couple of minutes.
Open the snips and place them around the neck of the intended victim. Close the pliers and check to make sure that you have clearance all the way around. You don't want to cut off the poor lads ears now, do ya.
OK, this is where the "touch" part comes in. Begin to twist the pliers around the head slowly. Enough pressure should be supplied to score the neck. Tread lightly here. DO NOT Squeeze the pliers or you'll end up with a big "V" in the neck and a ruined head.
Keep twisting and the head will begin to twist and before you are halfway around, the head will pop off cleanly.
I'll admit that it does take some practice, but it results in a good clean cut and no mess to tidy up with files and such.
Try it on some junk figures first. After 5 or so you should
be able to graduate to the real thing.