Karli-Rae,
No, never cut the fly line. You might try this but it is not a lot of fun and is time consuming but you will have the right amout of backing on your reel and your fly line will fill the spool closer to the rim. You strip all the fly line and backing off your reel. Take the front end of your fly line and start it on the reel and wind all of it on the reel. Then attach your backing and keep winding until the backing comes within 1/4" of your reel edge. Now pull all the backing and fly line off the reel and attach the backing to your spool and wind it plus your fly line onto the reel.
Not a lot of fun, but, it works....Hope this is clear and it helps
Warren
Fly fishing and fly tying are two things that I do, and when I am doing them, they are the only 2 things I think about. They clear my mind.