removing compression rings

I'm replacing a inlet valve for a stool and would like to know if there is and easy method for removing old compression ring.

No not without cutting the copper behind the compression ring, but by then the copper would be to short, then you'd have to add a little piece  of copper and on, and on, and on. So what I'm trying to say is reuse the old one, as long as it wasn't compressed to much, which would cause a leak. Good luck with your project!!!                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        r

Look at the compression ring carefully, it may not need to be removed if there are no dents or gouges in it....and if it is in bad shape, you have no choice but to cut the pipe and put a new one on because compression rings are just that, they compress around the soft copper and aren't meant to come off.