put something to sleep
• kill an animal, especially an old, sick, or badly injured one, painlessly (used euphemistically).
• "they took their pit bull terrier on a trip to France before having her put to sleep"
Similar:
put down,
destroy,
put out of its misery,
put someone to sleep
• make someone unconscious by using drugs, alcohol, or an anaesthetic.
• "a fast-acting barbiturate is administered through an intravenous line, which puts the patient quickly to sleep"