Kitten grooming

So I cut my kittens claws and at one point he moved so much I cut too much in and he bled but I didn't see it until an hour later, I'm so sad I love my kitten. How long till it grows back, it's very red

Kittens claws grow very quickly, so I would expect it will be fine in one week at the longest.  Be sure to watch out for infection.  Clean it after he uses the litter box, and you can even put some triple antibiotic on the injured toe.  He will lick it off, but in doing this, he will keep it clean.  If it should appear infected, i.e. running with yellow pus or the toe swelling and being unusually painful, you will need to take him to the vet and get oral antibiotics.