While the Bible nowhere explicitly addresses animal / pet euthanasia, there are definitely some biblical principles that apply. In Genesis 1:26 God declares, “Let us make man in our image, after our likeness. And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth.” Essentially, as the highest order of created beings on the earth, humanity has full authority over all other creatures on the planet. While having dominion over the animals includes the right to kill animals for food (Genesis 9:2), it goes far beyond that. We are caretakers/stewards of God’s creation. We are all, in a sense, to be shepherds over the creatures that share this planet with us.
The Bible makes it clear that we are to treat animals with dignity, respect, and mercy. Proverbs 12:10 states, “A righteous man cares for the needs of his animal.” The responsibility to be merciful to animals exempted man from the command to not work on the Sabbath day: “If one of you has . . . an ox that falls into a well on the Sabbath day, will you not immediately pull him out?” (Luke 14:5). The Bible also indicates that when an animal is a threat to people or other animals, it should be put to death (Exodus 21:28-35).
With these principles in mind, a biblical practice of animal / pet euthanasia can be developed. We are to be merciful to animals, and we have the authority to end the lives of animals. So, if euthanizing an animal would be a merciful act, there is absolutely nothing wrong with it. If we see an animal suffering, with no hope of recovery, the most merciful thing we could do is quickly and as painlessly as possible end its life. We are also free to do everything we can to preserve an animal’s life. But, again, when the time comes, and the most reasonable and merciful thing to do is to euthanize the animal or pet, it is absolutely a decision God has given us the authority to make. Figuratively speaking, sometimes the only way to get an animal out of the “pit” it has fallen into is to end its life.