First, if you are getting fur from a brick-and-mortar location and you have the ability to be at the cutting table, have the employee test the fabric to see if it can be ripped instead of cut. Ripping a straight line is a sure way to avoid messy cut fur edges, and the rip will always be square to the selvage edge—a definite plus when you work with the nap later. When ripping on your own, make a small cut through the selvage edge of the fabric. Then grab either side of the cut and rip away. Stop at the next selvage edge, and cut with scissors at that point.
When you are cutting furs, particularly the long and luxurious kind, we strongly suggest you don’t go in chopping with the scissors in a willy-nilly fashion. Instead, choose a very sharp pair of scissors, and with a lot of care, slip the cutting edge of the scissors along the base of the fur strands and only snip the mesh fabric, avoiding all fur. When done correctly, the result is a mess-free cutting zone and intact furry strands that make sewing a seemingly seamless puppet easier.