This is as true for insulation board as it is for the ubiquitous expanded polystyrene kind of foam used for everything from coffee cups to packaging material. Those stick-type hot wire cutters ...

The throw of the cutter is controlled by a stepper motor — partial closure nicks the insulation, while a full stroke cuts the wire off. The video below shows the build and the finished product ...

If you cannot cut through the wire insulation, or if you break the wire where you squeezed the wire strippers onto it, chances are that you are using the wrong gauge slot on the wire strippers.