I am one of those players who when I get rekt in lane, I can't stand mastery spam. so i think that muting an enemy should prevent you from seeing when they spam mastery or emotes to tilt you. It'll will help salty players get less salty (I hope).
I'm not sure if /ignore blocks their Mastery Emotes, however if it does then that's a simple solution, although it completely blocks out communication with the player and removes them from your Friend's List if they were previously on there.
If you're interested there are many "Custom Skin" modifications which disable Mastery Emotes completely. I can't post any links or advocate using them, as it runs the risk of "but this guy did it" and LoL has a no-modification clause in their EULA/ToS. I can say that's it's fairly easy to find with a simple Google search. The downside of this is obviously it is a third party program and always runs the risk of getting your account banned. While I've never used it myself (I enjoy the in-game taunts and Mastery Emotes myself, it gives freedom of expression and is super fun to show off your Mastery as a squishy target when you're eating a Malzahar Ultimate and know death is approaching), I've used many custom skins for years and have never had a problem. Riot has stated many times that MOST Custom Skins won't fall under the category of "game-breaking," however something which gives your Hitboxes a better chance of being seen or "zoom modifications" are clearly going to give you an advantage and is something you want to avoid - in this game and any competitive game, really. You'll also want to avoid exceptionally racist, sexist, homophobic, etc. (such as Nazi Teemo) things, as even though it's Client Side and only you will see it, leaving these things alone gives a certain "bad vibe" that most companies generally would not want to be associated with saying "it's cool." One of my personal favorite skins that I would happily buy if Riot ever launched is Pool Party Heimerdinger with Rubber Ducky turrets and bubbles for where the usual hexagonal pattern would be. There's no advantage given, and the enemy team sees you as a normal Heimerdinger, however the quality of life and happiness gained is immense, and often what Riot (and most companies) want to maintain by keeping their player base around.
Again, I can't advocate using any modification to the client or anything that directly reads the client's data (i.e. scripting) as it's clearly against the EULA/ToS, however I can recommend doing your research and trying to cope as best as you can with the Mastery Emotes. If you're able to disable them and it doesn't give you an advantage in any way - great! Other than that, it's going to be very difficult as you'll find a lot of players take great enjoyment out of the system. Take Elementalist Lux for example with her quote: "All the elements available and you choose to be salty!" Not to mention someone like Kennen who actually rolls on the floor laughing, it's difficult to ignore at times. Most of the time it's harmless in-game interaction and (most of) your opponents will often appreciate your interaction back with them. Take World of Warcraft for example, you won't necessarily be able to talk to the opposing faction due to the chat being garbled, however you can easily make a feast with a fancy umbrella and sit down to show you are a friendly character and willing to be civil.
One of my personal favorite quotes to spam is on Soraka with her sassy personality: "Yes, that was a banana. Chuckle, no one expects the banana!" Especially when you're throwing out these incredibly weak crescent-shaped yellow particles that deal almost negative damage.
Hope this helps, best of luck to you and I truly hope that you find the means of coping that work best for you!
http://forums.na.leagueoflegends.com/board/showthread.php?t=2436518&page=17#post27906871
type in "/ignore enemy", that stops emotes and taunts as well as muting them.
