A: No doctor in his or her right might would amputate a finger to get a ring off. There are always ways. I’ve not only seen Ti rings that were cut off in emergency rooms (and then had to tell customers they’d have to replace them, since I couldn’t just solder it together again…), but I’ve cut and diced into a few of them myself for various reasons. Some are softer than others, and they tend to be a bit tough to cut, but the ring cutters will do it. So will bolt cutters, which many emergency rooms also have around. Some titanium is indeed pretty hard, but it’s not all that hard. Most of it, you can cut easily enough with ordinary jewelers saw blades, though they tend to dull quickly…

Of more concern than the TI rings, to me, would be the advent of tungsten carbide rings. These would only be cuttable with diamond or similarly hard grinding tools, and I don’t know if your local emergency rooms would have a Dremel tool and diamond disk around…They can no doubt somehow still be removed, but I’d wonder how an ER doc would prevent further damage to the finger while smashing the ring with a hammer to shatter it, since that’s the most likely means I can think of at the moment.