Tungsten rings are a bad idea if your ring needs to be cut off. If you ever injure your hand/fingers wearing one, remove all rings immediately, but especially a tungsten or other hard metal ring.
FYI a tungsten carbide ring, although it cannot realistically be cut off your finger, is brittle, and can easily and safely be snapped with a pair of locking pliers (locking to avoid clamping down on your finger). You may be thinking of titanium rings which are not removable in this fashion and thus are less safe.