Mute, start using it. I know a lot of people don't use it, because the other player will almost argue back 99.9% of the time.
Just accept that you will get bad games, and unlucky match making, it's what you signed up for playing this kind of game.
I have some what of a grip on my anger, but league does seriously draw the most out of me compared to everything else..
If it really does become a problem, maybe just quit lol. Never look back.
Whats your reason for playing? you don't really have anything to prove, unless you're Diamond trying to become Master.
Even then, you should ask yourself what purpose do you have for doing it, and if the sacrifice will be worth the reward in the end.
Be rational, be a loser, whatever it is.. just keep your mind healthy and swallow your pride.