The few times I have had to cut foam rubber, I used a sharp knife and a T-Square.
For the knife I find a box cutter, razor knife, or Exato works best.
Use the T-Square to compress the foam rubber, then cut. As long as the knife is sharp there shouldn't be too many ragged edges. And these are items that are found in most homes.
I have also used a large ruler in place of a t-square. Just make sure that the surface you are cutting on is one you don't mind getting marked up.