Do you know something about "mercy-killing"?

It is usually refered to as euthanasia.

Euthanasia is the practice of ending the life of an individual or an animal who is suffering from a terminal disease or a chronically painful condition in a painless or minimally painful way either by lethal injection, drug overdose, or by the withdrawal of medical support. Euthanasia is a controversial issue because of conflicting religious and humanist views.

hi,

I wanted to know also why do some people practiced this mercy - killing...? in my own idea no matter how they called it, it is still killing..and for the person in his case is likely called suicide..

yes your right up to now it is still a big issue on religious and humanist views...