Why I'm inclined to do something that I know will have high mental stress for me

You love person X. He wants you to do Y. You know that doing Y will cause tremendous stress to you. But, still to make X happy, you offer to do Y.

I'm feeling this as a suicide but yet I'm compelled by myself to do it. Can anyone explain it, what kind of issue this seems to be?

Fear of losing person X is the first thing that comes to mind. However if person X really would leave you for standing up for yourself than you are not really losing much. Personally I would not do what they requested just to see how they react. The conversation that comes after is what really matters. Do they say "okay" and carry on as if nothing happened? Do they get all defensive and say "You would do it if you loved me"? Do they say "Why won't you do it"?
Base the future of your friendship on how they respond, just be sure to tell them why you are doing so to give them a second chance if needed.

Another catch in this situation. Even if you do Y, still person X will leave you. And you feel you should give one last happiness to person X. Knowing well in return what you are getting is misery