Ok, my Gizmo has a very hurt paw!

He has broken his nail about a quarter of an inch from the base. It's bleeding a tiny bit and he won't put his foot down. What should we do?? We put him in a crate where he is NOT a happy camper at all. He is hurting himself in there too as he never goes in a crate and it throwing a fit! Should we cut the nail off? Would the bleeding stop?? Poor boy!!!