Pliers won't cut jump rings that will sit completely flush when closed. A jeweler's saw is the way to go, though even faster is the Koil Kutter:
https://www.youtube.com/watch?v=HqdNbWAu1GkI started using mine with a Dremel when I was first starting out years ago, and now need to purchase an attachment for my flex shaft. I love it. It paid for itself quickly when I sold my extra jump rings as destash.