I've had good luck using a pair of pipe cutters.
First a rotating cutter to crimp the blade (and sometimes cut through):
Then a ratcheting cutter to cut the film and any leftover blade.
My exact process is to cut as deeply as I can with the rotating cutter.
If I haven't cut through the Polycarbonate, I'll use the ratcheting cutter to cut the tube - ratcheting enough to score the remaining tube without cutting the film. I'll twist the blade around at this setting until the bottom piece of tube separates.
Then I pull the bottom just a hair to loosen the film. Use the ratcheting cutter to chop through the film. Push the film back in.
The crimped bottom of the blade keeps the film in place without any glue. Though if you're the type that likes gluing film in place, you're free to cut the film extra short and glue it in place.
EDIT: I wouldn't recommend a saw, simply because you're likely to create dust that will get stuck in the blade and disturb the lighting.