Yes a vet can refuse to euthanize an animal.
A vet office is a private business and has the right to refuse to perform a service if they want too and you're free to go to another vet office to have the pet or animal euthanized if one vet refuses to do so.
I've known a few vet offices who did not believe in euthanize animals because they wanted no part in killing of the animals they loved.
So they did not euthanize animals and that's okay because you could take the animal to another vet in town to have the pet euthanized.
Some vets will just refuse to do something which is the vets right to do so.
If one vet refuses to euthanize your animal just ask around or call other vets in town and they will usually do it for you.