Question: I recently have had a discussion about my friend's tone in his email.

His supervisor asked him whether he wants to attend a summer school in May. He wanted to thank him for his invitation and also wanted to keep the mail short. As a result, that is what he came up with:

> 
> Hello Professor,
> 
> 
> I have plans during that period. Thanks, but no thanks.
> 
> 
> Regards,  
> 
>  John 
> 
> 
> 

He is getting along well with his supervisor, but I believe that the phrasing is a bit disrespectful nevertheless. It might be the case that I am not a native speaker. 

Am I exaggerating the situation and this is something can be overlooked?

Answer: 
"Thanks, but no thanks" is a sarcastic insult, plain and simple. If I were the supervisor, it would end any feelings of good will I had toward the student. From then on, I would provide the student with the statutory support required by my contract, but no more, and devote my energy towards helping other students.

A sincere apology might put things right.
I believe the phrase becomes significantly more polite by adding a simple comma, implying a different intonation:

> 
> Thanks, but no, thanks.
> 
> 
> 

Still, I agree with the other answers that this is uncommon style. In this case, it's not necessary to repeat the decline (`but no`) or the `thanks`.