I generally never mute anyone because we can always find a way to work together and have teamwork in the end, sometimes you just shouldn't speak for a bit tho until you make a good play together.
Also it's critical that, at this point, you don't rage at anyone at ALL, then you just make the game worse. Don't try to make jokes or anything that can be turned against you. DONT TILT!!!!
Also, play safe until you can make a big play with your team.
Once said play is made, trust is being restored and use the play to rebuild teamwork. If said play never happens, just apologize for raging (sometimes even if you didn't), and try to move on. THERE IS ALWAYS ANOTHER GAME TO BE HAD.
That's my idea of what you should do in these situations. Happened a while ago in a game I was playing mf and got angry at shac for not ganking when we needed him and he was nearby. We won that game.
TEAMWORK OP! :P
If a teammate is just being toxic off the bat for no reason ( not playing bad, getting role, etc), then there's not much to do...
Just try to have fun with it I guess.