"My aunt is smart, she is a teacher."
I don't think 姨 can be used alone like that. The word is 阿姨. The 的 is optional for family relationships, but it's better to leave it out.
Doesn't 很 mean "very"? Wouldn't that change the meaning of the sentence to "My aunt is very smart."
Technically, 很 means "very", but that meaning is often de-emphasized. So, 她很聪明 can be understood as just "she is smart". If you want to emphasize how smart she is, you could say something like 她非常聪明. (非常 = "extremely")