Plaskolite is a manufacturer of many, actually dozens, of plastic sheet products. Tuffak is a polycarbonate brand of theirs that is made in several versions, each having different characteristics. Same with their acrylic brand, called Optix. Do you know which product you actually have?
Sounds like you are cutting crosswise in a panel saw. I don't think it should matter whether you support the off-fall piece at the top during cutting.
The type of edge cracks you describe is characteristic of cutting polycarbonate with some saw blades. People mistakenly believe that polycarbonate cannot crack, but it can. It is resistant to blows to the face, but it can be cracked at its edges during cutting. Find out exactly which product you have, whether it's one of Plaskolite's acrylics or one of their polycarbonates. I have known salespeople at suppliers who didn't understand the difference. There also exists high impact acrylic which may have characteristics that differ from regular acrylic.
Plaskolite has downloadable guides for fabrication and painting of all their products. Visit their site. The guides and manuals are under the heading, RESOURCES.
At the shop where I work, the fabricators usually cut polycarbonate with a router bit, though I know it can be done with the right circular saw. They cut acrylic mostly with carbide-tipped circular saws. I have never known of a problem caused by not hanging on to the drop piece.
Brad in Kansas City