Cutting rings for maille jewellry, especially in precious metals can be a challenege. When you're crafting something to be worn close to the skin, good cuts and closures are invaluable for the pure feel of the finished weave. If you're selling a piece, bad closures and sloppy cuts in something like Argentium or Fine Silver aren't going to catch any eyes. So what's the answer?
Read the title already.... Put down the wire cutters and find a jeweller's saw. It resembles a small hacksaw frame with thumbscrews. Don't try and use hacksaw blades with it, if you can mount the blade at all, you'll just wreck your rings anyway.
Some hobby stores have them for... in my opinion, way too large a price tag, but if you're unwilling to wait that's an option. I ordered mine from TRL and it's perfectly suitable for cutting rings. Blades are less than a few dollars a dozen, get a lot, you're likely to break a few. I prefer size 4/0 or 2/0 depending on the wire gauge I'm cutting. You'll need some kind of lubricant, beeswax seems to be the standard. I use the parafin wax that most cheese wheels come coated in, it's free if you like cheese.
Second, get yourself a jeweller's vise. Not a small bench vise. Where a bench vise secures your work by applying pressure between the jaws, and you risk crushing a coil; the movable jaw on a jeweller's vise secures by applying pressure to the body of the vise itself. This means that your can clamp something hand tight and lock it in place. I took a few pieces of masking tape folded cardstock to pad the jaws and prevent scratching, and help secure my coils.
If you're all set up, time to string your blade. If you have an adjustable frame saw, crank down that top screw first. Then loosen both the mounting screws. Look closely at your blade, the teeth cut one way, and glide the other. You want the cutting action to be when you push the saw forward, so the friction doesn't cause you to pull open your coil. Lock the blade in it's mount closest to the handle.
This is the tricky part, you need a little tension on your blade. So place the handle against your abdomen blade up, and lean forward with the other end of the frame against your bench, so it very slightly compresses the "[" shape of your frame. Now lock the far end of your blade in place and relax.
If you've done it properly you can pluck the blade like a guitar string and it will ping without buzzing or sounding dull. If it does either of those things, re-string it or you're just going to break a blade. Run your chosen lubricant across the blade a time or two, and you're ready.
This is the most important thing to remember when cutting: let the saw do the work, you don't need to press the blade down into your coil, it will cut perfectly just gliding along on it's own. There's a sound associated with cutting sheet metal by saw, but when your coils are secured this way that sound is muted. Listen carefully for something that resembles a slide whistle, up and down, as you cut. If you hear too much scratching rather than ringing, it's time to re-lubricate the blade, and while you're at that check it's tension again.
When you're done, and have gotten over admiring your new cuts. Unstring your blade, I left one overnight once and the blade broke while I was asleep, the springback of the frame recoiling cracked a glass candle holder on my desk. Stupid, stupid way to wake up...