Decapitating A Human's Head Without An Axe Or A Large Knife?

In the elevator scene, he only had some sort of metal wire or something in his pocket that he used to choke people around the neck. Yes, that can kill, but can the head really come off with that piece of wire? The scene doesn't look too realistic in that sense, at least to me. It takes a large axe and perhaps several hard chops to break the bone structure, or a large knife or sword to perform a similar exercise. It is certainly not easy to perform decapitation with a thin piece of string or wire? Also, the wire that Martin carries doesn't seem to look like it's made of steel but a nylon or some other material, which will not be able to cut through the flesh too easily, not to mention the spinal cord.