Styrofoam is easily cut by a hot element, in fact professional cutting applications are done by hot wire cutting rigs. The basic element of a foam cutting knife is a hot wire or blade that can be passed through the foam. To make your own hot foam cutting tool, all you need to do is attach a heat source to a wire that will hold the shape you want.
Stretch the wire to twice the length you want for your hot knife, plus 6 inches. For example, if you want a 5-inch knife, stretch the steel wire to 16 inches long. Fold the wire in half so there is a sharp bend in the middle. Cut off any excess wire.
Twist 3 inches of the wire around the top lead on the soldering gun and three inches around the bottom lead. Use the needle nose pliers to secure the wire firmly to the soldering gun.
Plug the gun into the wall and wait for it to heat up the wire. Cut through the foam with the steel wire "knife" you created. Unplug the soldering gun when you're done using it.