The best way to cut acrylic without using power tools is by using a scoring blade. Usually places like Home Depot sell acrylic scoring blades at the same place they sell their acrylic. Also, in the hardware department they usually sell scoring blades designed to fit into utility knives.
The scoring blade has kind of a hooked edge to it which you draw across the plastic. As it cuts it will actually gouge out the plastic. You need to score it repeatedly [using a firmly clamped straight-edge] until you're at least halfway through the acrylic.
Then, holding the larger side of plastic flat on a larger surface like a table, use your hands or a pair of pliers to grab the other side [waste side] and quickly snap downwards - the whole piece should come off in one piece. I've had pieces break before where they don't all come off in one piece, but if you've scored deep enough you won't crack the piece you're trying to save.
If it didn't break cleanly use your pliers to snap the rest off and then use sand paper or an electric sander to smooth out any rough edges or any 'teeth' sticking up from where the piece broke unevenly. Cutting acrylic is tough but your best results will come from patience - just really score heavily into that piece before you go to snap it.
-----
Matt Campbell
Big animals, little animals, plants - right down to the sea itself. We need them, not just for their own sake, but because all this has to be here for everybody forever. Only one thing is certain: if we are to preserve our environment and save this priceless wildlife we need much, much more knowledge.
Harry Butler from 'In the Wild With Harry Butler' 1977