Not sure of the type of plastic,shape ect. but you can use a wire to cut through plastic by simply heating it with an electric current.
A couple of aligator clips,some heavy "lead wire" and a thinner cutting wire and a power source is all you need. However the "hacksaw" wwill work and a sawsall with a metal blade will make short work of it. Amother method would involve a trim router but as you said you dont have the tools.
I worked with acrylics for awhile and we cut it with various things depending on the thickness and what needed to be done,cutting with a heated wire let you make bandsaw type cuts that were as smooth as the product.