These wire strippers make clean cuts without inflicting damage.
The cutters are effective on fine telephone wire or 12-gauge copper wire, as well as harder steel baling wire. If cutting through wood is important to you, the saw blade is up to the task.
Those stick-type hot wire cutters from the craft store that plug into the wall aren’t much better than a knife. The actual cleaving of foam is easier, but dragging a long, hot flexible wand ...
While there are all sorts of ways to build a hot wire foam cutter, this design from [jasonwinfieldnz] is both interesting and imitable. If you don’t already know it, nichrome wire is nifty stuff ...