Couldn't you just shatter the diamond with minimal risk to the actual finger?

Probably. That's how they get tungsten carbide rings off.

I was rotating the carbides on a wood planer and a couple of them were held in by machine screws that weren't budging. I called Byrd, and their recommendation once you've stripped the screws is to shatter the inserts. I put a crappy chisel underneath and whacked it with a hammer.

I can confirm that it works. I heartily recommend a face shield, and I wouldn't want to be the first guy the doctor had to break a ring off of.

Other than a few comments on Reddit, every jewelry site that I've looked up says that stainless steel can be cut off with regular ring cutting tools.

The biggest difficulty that I know of with it is that the material is not very workable, and so if you need to get the ring resized, you may be out of luck.

A Dremel with a regular cut off wheel would cut right through titanium.

>I saw a video of someone making a ring out of polycrystalline diamond and…if that gets stuck for some reason, it's never coming off.

Diamond is easy to remove: it'll melt with a blowtorch.

(You didn't say the finger had to be preserved intact...)