Toes and feet can bleed a surprising amount. A sow here with chronic bumblefoot ripped off a scab a couple days ago and the amount of blood was quite amazing. By the time I got the bleeding stopped and the foot washed/salved/bandaged - it looked like somebody had been slaughtered in my bathroom.
So, if you´re going to cut the nail off - I would wait until the vet clinic is open just in case you need their help. If the nail is mostly broken off and "hanging by a thread", it is probably best to cut it off. Be prepared to spend some time cleaning the foot and stopping the bleeding afterwards though.
Most likely you will be able to stop the bleeding simply by applying pressure. Sometimes it helps to use a cloth rinsed in cool water and wrung out. Once the bleeding is stopped, soak the toe for a couple minutes. Warm water diluted with Betadine Solution (1 part Betadine/10 parts water) would be the best thing. If you don´t have that, you can soak it in mildly soapy water - then rinse well. Apply a small dab of antibiotic cream, and then watch Clint closely to see if the toe starts bleeding again, or if Clint is licking/chewing at it. If either of these things happen you might have to bandage the foot for a couple days while the toe starts to heal.
If you can´t get the bleeding to stop (which is unlikely, toe bleeds are usually not that serious), you´ll probably need some silver nitrate sticks or solution from a vet. This kind of cauterizes the wound and stops bleeding.
You will need to wash or rinse Clint´s foot and apply ointment for a week or so until the toe is well healed. Watch closely for swelling, pus, signs of pain - which could indicate an infection. If bedding debris is bothering the toe or keeping it dirty - you may have to keep Clint on towels for a few days.
Bacitracin or Triple Antibiotic Ointment are fine as long as Clint isn´t ingesting a lot of it. The neomycin in these ointments can cause digestion upsets if much of it is eaten. If he is licking/chewing the ointment off - you´d probably better call your vet and see what they´d recommend.