Cat ripped his claw out

One hour ago I found blood spots all over my bed, right where my little angel sleeps next to me. It took me another hour to figure out it was one of his claws, greatly scaled back farther then I would ever dare trim them. I assume for whatever reason while grooming next to me he went way too far biting one of his claws.
The vet is closed now, not that I am in a hurry for another costly emergency apt since he is not limping, is still quite hungry can I assume if I clean the area with a watered cotton ball that would be enough until his previous Nov 5th appt? What would a vet do for $100 cost anyway but tell me its going to grow back eventually(I hope) My only concern is the litter box, sand, infection..Thoughts?

Clean it with saline - boil some water and add a teaspoon of salt (preferably sea salt but table will do) to an imperial pint {20 oz) of the water, let cool to body temp and wash the foot. Don't put peroxide on it though, as that eats good tissue as well. Just keep it clean until you can get to the vet if you think the injury is bad enough

This can be a serious injury. You said it looked like the nail was chewed down? Chances are that something happened, either he was caught up on something, somehow injured his paw and/or has a preexisting infection that is causing him pain and irritation where he would excessively groom the area to release the pressure. When it looks like they are chewing on their claws, they are cleaning the cuticles and peeling off the excess layer, actually part of sharpening their claws.
I would call your vet and ask for advice, maybe they can move the appointment up......