If we exclude the stronger phonetic stuff we get:

“t’a fermes-tu, ta gueule?”

short for

“tu (l)a fermes-tu, ta gueule?”

Which amounts to something like “Will you shut it already?!” given that this sounds like it was screamed angrily (and would still be pretty damn rude), I wouldn’t feel bad about adding an f-bomb in the English translation either. Ferme-la! or la ferme! would be the more neutral forms. (I’ve never seen bouche show up in this context.)

As for the phonetics, it is common for /l/ to drop in pronouns if the vowels isn’t a schwa. (Cf. /i/ for /il/). This promptly elides into “t’a”. /ɛr/ or /ər/ to /ar/ is a very common sound change in informal Quebec French (e.g. charcher), while -tu is an emphasizer in questions.

I’m not sure what’s the backstory of /yeule/ for gueule, but it’s a standard lower register pronunciation, and generally palatalisation in front of a front vowel is hardly surprising.

Being a French Canadian, I think I can help on that.

T’a fermes-tu ta yeule?

Between this sentence and your “France French” translation, the only real difference is yeule. This is deformed word from gueule, which means an animal mouth (pejorative for a human).

T’a is a shortened tu la. This is the same as Je suis which often is shortened to J’suis, Chuis or even Chu like in this next sentence :

Chu ben tanné d’écouter ses jokes plattes.

Fortunately for foreigners, Quebec made a website that explains all of our Quebecisms.

Good luck!

“ta farme tu ta yeule” est une contraction de “tu la farme tu ta yeule”. En français standard on voit qu’il y a un “tu” de trop et on devrait plutôt écrire “la ferme tu ta gueule”.

Plus souvent en québécois on va plutôt dire “farme ta yeule” ou plus simplement “ta yeule” qui en français parisien se dit “ta gueule”.

Yeule : Mot québécois qui fait référence à la bouche. C’est une déformation du mot “gueule”, c’est donc un mot assez familier lorsqu’il est utilisé pour un humain.
Par exemple, lorsqu’un québécois te dit de “fermer ta yeule”, il te demande de te taire !
La définition complète est ici : http://www.je-parle-quebecois.com/lexique/definition/yeule.html
Toutes les définitions des mots québécois sont ici : http://www.je-parle-quebecois.com/lexique.html