Euthanasia

Euthanasia (from Greek: εὐθανασία; "good death": εὖ, eu; "well" or "good" + θάνατος, thanatos; "death") is the practice of intentionally ending a life to relieve pain and suffering.

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Abolfazl Sabouri, Abolfazl Sabouri is based in New Zealand and has an MA in Jurisprudence and Islamic Studies. He is a graduate of Elmiyeh seminary in Qom with more than 15 years of study and research where he has... Answered 1 year ago

It is not allowed. Our body and soul are a trust from God and the time of death is in His hands.

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Zaid Alsalami, Shaykh Dr Zaid Alsalami is an Iraqi born scholar, raised in Australia. He obtained a BA from Al-Mustafa University, Qom, and an MA from the Islamic College in London. He also obtained a PhD from... Answered 1 year ago

Bismihi ta'ala

This would depend on the recommendation of a veterinarian or evaluation of a qualified person, as to whether the animal should be put down or not. If they believe that the animal pet should be put down, then it would be permitted to do so. 

And Allah knows best.