Visit http://stemlynsblog.org/the-undertakers-ring-method/ for more information.
This is the undertakers trick. If you have arrived here then don't forget to visit the StEmlyns blog as well for more posts on EM topics.
2 caveats about this....I say that I've never cut a ring off. Sort of true as others have done it for me in two circumstances. 1. If there is a deep wound to the finger distal to the ring this is not a great method 2. If the ring did not come off before the injury due to bony (i.e. fixed) enlargement distally then clearly this won't work. However, if they were able to get the ring off that morning, and now they cannot because of soft tissue swelling, and they can tolerate the discomfort of the procedure then this is a great technique.
Check out the better explanation here http://stemlynsblog.org/the-undertakers-ring-method/
And obviously, this is best done by someone who knows what they are doing, and you try it at your own risk.