Couple ideas...
Hot knife by Micro-Mark...et al.
Old set of electric oscillating/serrated carving knives. Or, an old, dedicated long serrated blade 'bread' knife.
I say "old" on these, because mama won't be happy if you use her best cutlery from the kitchen. Cutting foam accelerates dulling of the blades. Sure, you can sharpen them again, if need be. But home diplomacy will be enhanced if you get your own....garage sale, discarded (with spouse/parent blessing) kitchen tool, dollar store, etc....
And serrated knives will not create the fumes that a hot wire/knife will...requiring good ventilation!!!....but they will make some dust that an appropriate shop vacuum/filter will help control as the carving goes along.
I've used both types of the above knives on pink, blue, and beaded white Styrofoam. They work well.
FWIW....
KD
