EVA - https://en.wikipedia.org/wiki/Ethylene-vinyl_acetate

Think foam kneeling pad, flip-flops (the non-electonic kind), foam garden slipons, etc.

I would think the removal of material requires a sharp thin edged tool with no teeth, a thin wall tube sharpened to a razor edge that cats more as a punch, perhaps with a small rotational force back and forth, but as you said, it will grab and heat will build up and then it gets worse.