Определение put something out of their misery в Английский Язык Английский Язык словарь
to kill an animal because they are in a lot of pain and you want to end their suffering. - "Both of its back legs were shattered and I figured the kindest thing would be to put it out of its misery with a bullet."
to stop someone worrying, usually by giving them information that they have been waiting for. - "I thought I'd call her with the results today and put her out of her misery."