You can easily shatter it with a vice grip or locking wrench, and with the rise of tungsten wedding bands EMTs and hospitals are more and more equipped for this.

Don't cut, shatter. Grab some channel locks and be free.

Vice grips would probably be your best bet because they allow you to adjust the diameter they grip at fairly precisely hopefully avoiding further injury to your finger (such as: embedded tungsten fragments).

I use channellocks, the width setting feature accomplishes the same goal, using vice grips takes too long. But do you, I suppose.