Hi, Michelle. I just finished doing a couple of sheets of Lexan (similar acrylic plastic) to make customized viewfinders in a "golden ratio."
: the easiest way is to use a "Plaskolite cutting knife" or similar tool. It's a plastic-handled razor knife that cuts when you draw it toward you, giving you more control. Looks like this:
You pull it along a straightedge on the plexiglas deepening the score mark with each pass. When you've cut through about half the thickness, you can snap the sheet on the score on the edge of a table. They vary in price but mine was about $4 at Lowes.
: Yes, you can polish the scratches out, but what I do is get automotive Turtle Wax, smear it on the acrylic sheet, wipe off, polish with a soft cloth, and repeat five or six times. The transparent polish gradually fills the scratches. Much
easier than gradated abrasive paper.
By the way, Turtle wax works marvelously on scratched CD's and DVD's, too!
Hope this helps--I always love salvaging found "treasures."