Thoughts on euthanasia for animals suffering from incurable conditions?

My aunt just found a badly injured cat (road accident). Won't describe the injuries but it's pretty much beyond any medical or surgical intervention. This was the vet's opinion as well. When my aunt asked him to euthanize, however, the vet has refused (we live in a Buddhist majority country, and many people are religious about things like this. Most of them don't have a problem eating chicken or fish though. But that's another discussion)

The same thing happened a couple of year s ago to my boss. His dog, who was very old, had end stage cancer. He tried calling dozens of vets trying to get the dog euthanized because the poor thing was in so much pain but no success.

So I was wondering what's the opinion of other vegans regarding this? I feel like om one hand we'd be helping the animal to ease the suffering, but on the other hand since we can't communicate and get consent, we might be doing something the animal doesn't want. Thoughts?