Nope. Your cuticles are there for a reason... and a good one at that. They protect the developing nail and surrounding skin from bacteria, so cutting your cuticles is definitely not a good idea. Doing so will heavily increase the chance of infection and, in case you didn't know, infections in and around the nail bed are not only unsightly, they are very painful.
If you are a true cuticle hater, try pushing them back with a cuticle pusher - I find steel cuticle pushers the easiest and most effective type to use. If your cuticles are too dry, hard, or tricky to push back, try using a cuticle cream or cuticle oil to soften them. I recommend the Dadi'Oil Nail Treatment (£11.95 nailpolishdirect.co.uk). Although it is designed to treat weak and brittle nails, this luxe oil helps keep cuticles hydrated, well nourished, and easy to manipulate.