The best call is always to see a vet for a formal assessment. Open wounds can always lead to chances of infection, and especially on an Angora, you really can’t get a full picture of what the wound looks like.

I would also recommend going to the vet in general because she is a new rabbit and she should be checked out to ensure she is healthy.

Be sure you go to a rabbit-experienced vet. They are almost always exotic vets, which is a special classification of vet, trained specifically for non-dog/cat animals, as many procedures and medications safe for dogs and cats are very dangerous for prey species, like rabbits.

Unsure if it’s a typo, but do you multiple Angora rabbits, or just one? “I just got my first German AngoraS…”

How is she doing? Did the cut heal over well?

Rabbit skin is extremely delicate and easily snipped as you have found out, to help prevent this next time you clip them use a comb and comb it through the fur and keep it placed between the skin and the scissors for each cut so that it prevents you from being able to clip the skin.