It would be MUCH better to remove the sprocket with the cam still in the head. Putting the sprocket in a vise is asking for trouble. It would be much better to lay the sprocket across the open vise jaws with the cam pointing down, but it is still a poor choice. It does not take much to separate them if you do it correctly.
Isn't he talking about putting the pulley in the vice after it broke off? That is what I was reading. Trying to get the piece that was still in there out.