I am shocked! This is serious and warrants an investigation into the methods in that grooming salon.
I would not rest until I had lodged a complaint. Your dog was hurt. He was lucky you were there.
I have heard some awful reports of what happens with SOME groomers (not all, of course)
Certainly do learn how to trim your dog's toenails yourself. If you are unsure, then book an appointment with a vet or vet tech who can show you how to do it safely.
And always give your dog a treat after doing one foot, and then another little treat when you have done the other foot.
Hello~That groomer should be closed, she has no business working with dogs and treating them that way. I don't think all groomers are that way, my aunt takes her dogs to a groomer and they can't wait to see her, I truly think for the most part, they are good, compassionate people, I am sorry you had a bad one, I hope your dog is OK.
As to learning how to cut their toenails, it is always a good to know how, I would ask your vet to show you.