[daphne]

I've cut many dogs nails, I've worked in vet clinics and useally clip all of my friends dog's nails. Honestly your dog may not have started to bleed up on the table, and was fine in the cage, but sometimes once pups hit the ground it may grind off that last tiny bit and start to bleed.
Dont worry about it, I typicaly put corn starch on it, or if its not bleeding bad, and you can keep him in a non carpeted room the bleeding will stop on its own

[saz]

daphne is right the nail might not have been bleeding when the groomer was working on your dog. i have cut a dogs nails before and they havent started bleeding til later. it should be ok just put some kwik stop, flour or corn starch on the end of the nail.
are your dogs nails black because it can be difficult to see the blood line then.
if you were pleased with everything else the groomer did i would stay with them and just mention what happened next time you go.