Although people will understand you, we American speakers would not say this. However, a better way to say it if you have to is He breaks society's rules by making different mistakes. Not sure what society rules are. taboos, mores, etc.

Grammatically, yes, it is correct, but in terms of choice of words, 'different' isn't particularly necessary. He makes different mistakes. He makes mistakes. By drawing attention to the plural in the context provided by the first half of the sentence, the reader automatically assumes the aforementioned mistakes are different. The degree to which they differ is up to you to clarify. As an antonym one might say 'he makes the same mistake a lot' (or words to that effect). I would add that 'he breaks society's rules' vs 'he breaks the rules of his society' are (in the vernacular) only different insomuch that one is shorter than the other (that is, ease and speed of saying rather than making sense to a native speaker). The latter would be more the written form, or said in a more serious/dramatic tone/setting.