We did this last year to Beau, getting him ready for a champ show

!!! I used a styptic pencil, and it did stop the bleeding - I was worried that he would develop a limp, but bless, he was a good little soldier and was absolutely fine (one of his back paws).
He pulled back for a couple of weeks after that when we were checking his nails, but lots of fuss, praise and treats soon got him back to giving each paw ing turn :)
It's a lot more difficult when the claws are black - when they are white, you can see exactly where you have to stop.
Mind you, I would far rather cut a dog or cat's nails than trim a goat's hoof!!!
Margot