Literally : Even if you talk to him/her a lot more and finally wear out(破) your mouth, 。。。。 It implies that there is no need to waste time, energy etc. persuading someone. For example, if you want to attend a foreign school, company, but your mother don't want you to and speak a lot, Then your father may say 'Since she has made her mind, Even if you has worn out your mouth, she won't change that.'/'既然她已经下定决心，即使你说破了嘴，她也不会改变的.' Sometimes you may also see these sentences, 即使你磨破了嘴皮/即使你说破了大天/即使你扯破了嗓子.

-regardless what you are going to say like the other guys said, it literally means :"even if you talk till your mouth wears out" (破了嘴 can mean a few things, usually it is to the point of speaker too tired to say another word but it also portrays the analogy of blooded lips, swollen lips, general wear and tear of the mouth)

I am afraid that It is not a complete sentence . "你就是说破了嘴" is equal to an Adverbial Clauses of Concession. Here In this context, ＂你就是..."means "even if you ....." In literal translation, "你就是说破了嘴,..." means "even if you don't mind taking the trouble of ＂might get a broken mouth" just to talk me into something, I will not take it..." ＂说破了嘴" is an exaggeration. It is like that you are always talking without any break all the time so that your mouth finally gets tired and broke. Hope it would help you

it means no use to speak much more. 你就是说破了嘴我也不会听你的 means shut up.

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