One issue with cutting templates (for my router, etc.) out of plastic is the heat generated by the blade and the resulting melting (and, then fusing) of the material behind the cut.
I had a paper pattern spay-glued to the sheet of salvaged 3/16" plastic (from an old Staples Display Rack - great dumpster for "finds") and I tried spraying a lubricant ahead of the cut line. The paper pattern absorbed the oily/waxy spray and the cut material fell away leaving a clean cut behind. I had switched to a blade with fewer teeth (as I didn't have one of those plastic slicing blades on hand and thought reducing the number of teeth might do the trick before I thought of the oil spray).
THe stuff I used was foamy/waxy as opposed to the fine clear spray of a WD-40, say. I cannot say if WD-40 would have worked as well and cannot recall what the stuff I used was called. But The difference was so impressive that I thought to post it here FYI.