Are you sure you aren't getting confused between polystyrene sheet and foamboard?
Foamboard is the stuff with a thin plastic sheet on each side, polystyrene is just the foam.
I didn't even think they made foamboard thicker than 1/2".
Anyway, if its foamboard you want to cut, you are probably best scoring with a knife and snapping it, as already stated. A saw would just wreck the plastic
If its polystyrene sheet try and find a 'padsaw', they have very fine teeth, and look somewhat like a long knife. (Think stanley-knife handle with a narrow saw blade instead of a knife blade.)
Another alternative is to either get a foam cutter, or find a soldering iron or soldering gun that has a cutting attachment.