How can I cut a soup can to hack egg rings?

use a metal cookie cutter

I know I'm late to the game, but I've had success cooking eggs in onion rings. You should sautee the rings on one side for a few minutes, then flip and add the egg. Same with bell pepper rings, but it won't be as round

oldunc and Sam1148 are correct in pointing out that most metal cans (here in the USA), are not suited for this application.

These cans have molded bottoms with beveled edges which makes them easier to stack, both at home and on a store shelf. The bottoms of such cans cannot be neatly removed by a typical consumer-grade can opener.

Gone are the days of taking your fifty-cent can opener to remove the top and bottom off a tuna fish can.

I suggested the aluminum foil "art project" since this appears to be an experimental recipe for you.

If you find yourself making crumpets on a regular basis, by all means, buy a set of cheap rings at the nearby restaurant supply shop (or Amazon). You really don't want to waste your time hacking ad-hoc foil rings every time you make this recipe.

For easy storage, just corral them together with a piece of kitchen twine. You could also toss them into a paper bag as long as you let them breathe to prevent rusting.

Most of the cans today are round bottom cans. Useless for using for egg rings.
Try making a stir fry with water chestnuts and bamboo shoots. Those still have the non-rounded ends. So does some shrimp and crab.

First you have to cut the can. You will need a hack saw with fine teeth. Take the can and slide it over any scrap lumber a couple of feet long that it will fit over. Nail it through the bottom to the piece of lumber. This will give you something to hold on to while you cut it. Put the board across a chair, put your knee on it, and cut the can where you want it.

Slide the ring off. It will be sharp. File off the little burrs with a bastard file. Lightly tap the top all the way around until the top is bradded down and no longer sharp.

Now you have a ring. You have to treat it so it won't rust. Lightly coat it with canola oil and put it in a 300F oven for an hour. Do this every time you use it. Eventually it will turn black and won't rust much if you don't put it in the dishwasher. It will be ugly and homemade-looking and your wife will look at it every time she opens the gadget drawer and sigh. Then she'll look at the dent on the chair rail you made when you cut the can and sigh. And she'll comment how the kitchen smells funny from running the oven for an hour, kind of like garbanzo beans. Was that can ring thing you made from a can of garbonzo beans? And she'll sigh, and stare out the window and you'll know damn well that she's thinking about her college days when her and Chip would go get hummus at the Olive Road Bistro, and how Chip's Mom always had said, "Honey, if it can't go into the dishwasher, it doesn't deserve to live." And she'll turn to tell you this for the millionth time, but you'll already be in your chair with a stiff drink, grimly jacking up the sound on "Good Eats" to drown out the Uninvited Wisdom of Chip's Mom. You won't get up to go to bed until you're certain she's asleep.

http://www.amazon.com/gp/aw/d/B0000VONZ2/ref=mp_s_a_1_1?qid=1445038223&sr=8-1&pi=SX200_QL40&keywords=stainless+steel+egg+rings&dpPl=1&dpID=21C4ZNHTJ8L&ref=plSrch

Unless you have a metal working shop, cutting sheet metals cleanly enough for this sort of use is not really practical. Most cans now are made with molded bottoms that won't remove cleanly; as Half Pint noted, some imported products still come in old style cans. They're a bit small for crumpets, though, usually 3". You can get english muffin rings at Sur La Table or other places at about $5 for four, or you can sometimes find appropriately sized plain cookie cutters. Egg rings don't work so well because - don't remember why- I think when I was looking into it, all that I saw had a raised rim inside.

sure can. tuna cans might be better. it might also be good if you have one of those can openers that removes the ends without cutting the metal.

Not sure if rummaging through the recycling bin is something that you'd consider.

Personally, I would be inclined to hack some impromptu recyclable rings out of aluminum foil. I'd fold the sheet over several times for added thickness/rigidity and use staples to securely fasten them.

To me, someone with moderate handyman skills and basic tool kit, but no home shop, this sounds like a dangerous project for the sake of saving a few open cans. You'd probably need a powerful saw, and something to sand the edges of the cut cans.
In your place, I would empty a couple cans (tuna, vegetables, whatever), store or use those contents, and make the crumpets using one can ring for each.