couple of thoughts...
whichever method you use, leave the backing plastic on the perspex until the job's finished. It not only helps prevent scratches, it lessens the danger of the stuff fracturing on you too. Historically I back up the protection along the cut with layers of masking tape too.
As for cutting, it may be simpler (if the shape is pretty basic) to cut it by hand; using a sharp knife and straight edge, score a line along one face (similar to cutting glass). Pay particular attention to each end of the cut. Once scored, hold the piece over the edge of the bench, score aligned with the edge, scored side up. Simply bending the material will propogate a crack along the score line. Deburr the edges with a file, but be carefull, they're razor sharp.
I work with the stuff all the time, making covers etc.