Do you actually mean Styrofoam (dense, closed-cell foam, often pink, blue or black) or expanded polystyrene (white squishy beads pressed together)? The latter stuff is widely and incorrectly called Styrofoam, but the two things are quite different and advice for one doesn't always work for the other.

Expanded polystyrene (EPS) is virtually impossible to cut really cleanly without a hot blade or wire - the beads will tear out and the edges will snap.

Actual Styrofoam (XPS) can be cut nicely with knives etc. but if you have confused the two materials this could explain why you are having trouble.