An E-stop should kill motion and the hot wire instantly and safely. The most robust approach is a latching mushroom switch that cuts mains power to both power supplies (motors and wire) through a contactor or by breaking the supply input — when slammed, everything dies and stays dead until reset.
At minimum, wire the E-stop to drop the wire-heat supply (the real hazard) and disable the drivers. Avoid relying only on a software 'stop' command over USB/Wi-Fi, which can hang. Make it big, red, reachable without looking, and test it. Foam cutters are low-force, so the danger is the hot wire and mains wiring, not crushing — design the E-stop around cutting the heat.
At minimum, wire the E-stop to drop the wire-heat supply (the real hazard) and disable the drivers. Avoid relying only on a software 'stop' command over USB/Wi-Fi, which can hang. Make it big, red, reachable without looking, and test it. Foam cutters are low-force, so the danger is the hot wire and mains wiring, not crushing — design the E-stop around cutting the heat.