The Bible gives no view on pet euthanasia. The Bible was written for us but not to us. There are many subjects of concern and interest in our modern world that the Bible doesn't address. As John Walton writes, "Ancient Hebrew authors would not be expected to include content that might address social networks, climate change, party politics, capitalism, individualism, evolutionary biology, an expanding universe, nihilism, communism, consumerism, and so on — all the very aspects of our modern world. They could not anticipate Christianity, Islam, Hinduism, Buddhism, or any other religious system. We could not expect them to address, modern values, philosophy, medicine, economics, or politics, or to understand how we think about history, science, or law, let alone our views about reality or existence."

I will add to that, however, that the Bible teaches we should not be cruel to animals (Prov. 12.10). Animals have worth and dignity (Ex. 21-22.14; Dt. 25; Lk. 12.6), though not the same worth as human beings. Given that we are to be caretakers of nature and not abusers of it, I would say that it's a judgment call on your part whether ending the life of a suffering animal is being cruel or kind. My opinion, but it's just my view: Animal euthanasia in your illustration is kind.

Please provide biblical passages in support of your answer.

Question:

I recently got into a car accident with a deer

If I found out that this poor animal survived and was suffering would it be wrong of me to end its life?

There was no way we could have taken it to the vet as we didn't have a large enough car, and the car was completely totaled.

Besides we we about 30 miles from the nearest vet.