To keep the rings round, you will need to twist the ends open; never simply pull them apart. If you do pull the ends away from each other, it is very difficult, if not impossible, to get the ring to lie flat.
You will need to hold the ring with the cut ends in the 12 o'clock position and have the ring firmly grasped on either side. Try and cover as much of the ring with your pliers as possible to avoid twisting the ring out of shape. One end of the ring is pulled toward you