Use this phrase to check your guess about something and show your surprise at the same time.
For example, imagine that your old friend from college who you haven't seen in 10 years has a son, Nathan. The last time you saw Nathan, he was 4 years old. Now you run into your friend on the street and she's with a young man who looks a little bit like your friend. You can say:
Don't tell me this is Nathan!
This means "This is Nathan, isn't it?" as well as "I can't believe this is Nathan!"
Here are some more examples:
Don't tell me you're tired already!
Don't tell me you've never seen "Titanic"!
Don't tell me there's no peanut butter left!
We use this expression in spoken English, not in writing.