At some
point, if you
make enough jewelry, when you're nearing the end of a project you'll
run out of jumprings. To cut more rings I use a jump ringer cutting
system which is powered by my Dremel® or flex shaft. They're a
pricey investment. So unless you are cutting LOTS of rings, you can
either use a jewelers saw, which cuts both ends of the ring flush at
the same time, or you can use the simple method shown below.
The
first thing you'll need to do is make a wire coil.
NOTE:
When making coils it's best to use a metal mandrel as a wood mandrel is
soft, allowing the wire to cut into it which will make the coils
inconsistent in size and difficult to remove from the mandrel. Knitting
needles work nicely for this. I've used 16 gauge wire
in these photos.

Cut
the coil with your flush cutters. Be sure to cut your rings in a
straight line across the coil. To ensure that your jumprings close
without a gap you'll need to cut both ends flush as shown in the last
photo.
Flush
cutters only cut a flush edge on one side of the cut.

So, after making your
initial cut you must go back and trim the "V'd" end flush as shown here.

Voilá! Here's your finished jumpring.
This method works great in a pinch. Tumble your jump rings to remove
any burrs and give them a wonderful finish. This also hardens them
somewhat.