Clipping the cuticles should be the last resort and should only be done if it is visible on the nail and in excess or if you have hangnails. So what is cuticle? In simplest form, it is a thin layer of skin that covers the nail plate and the by product of the eponychium. It is there to protect the base of the nail and nail matrix from bacteria and infection. People often get manicures to remove the cuticle and with the proper implements it can be removed for cosmetic reasons. A cuticle pusher and solvent typically does the job for removing excess cuticle and buildup.
Hangnails are hard pieces of keratin/skin and can be painful and cause infection if not removed. Cuticle nippers are great for removing hangnails if used properly. Applying a cuticle oil regularly will help keep hangnails at bay.
Ultimately the decision to remove excess cuticle is that of the client and with the right tools and a trained hand, you should be just fine. Enjoy your manicure!