That sentence can be used in different situations.
1. When you are trying to make a guess and you want the answer to come from you and not from your listener/s (ex. I think the answer is... Wait! Don't tell me!)
2. When you find something hard to believe (ex. Don't tell me you want to leave me?!)
3. When you simply have no interest in knowing (ex. I don't care, so don't tell me!)