Is the question "Would/Could you mind your own business ?" a polite way to say "Mind your own business !" ?
There is no 'polite' way to say, "Mind your own business". More polite ways to say the same thing are numerous and varied, depending on the situation. Some possibilities:
1. "This is a private matter between ____ and myself. Would you excuse us please?"
2. "I appreciate your interest, but I prefer to handle it in my own way."
3. "I want to try it my way but, if I need help, I know just where to turn."
4. "Go peddle your papers!" could be said to be just as firm, but slightly less confrontational- more jokingly.
Post #2 has some useful suggestions. The second is pretty firm.
I would say that any sentence which includes the words "Mind your own business", even if preceded or followed by other words, would not be described as "polite" to any extent.
NOT A TEACHER
(1) As the teachers have said, there is no polite way to use the words "mind your own
business." (For some people, those are "fighting words.")
(2) Actually if you really want to send a "strong" message without being
openly rude, you can always use the ultimate "weapon": SILENCE.
(3) For example, if someone says something that you feel is putting his/her
nose in your business, simply smile and say absolutely nothing. He/she will soon
get the message that he/she is out of line. Silence is powerful and terrifying to us
human beings.
(4) If someone writes something to you that you feel is out of line, simply do not
dignify it with an answer.
NOT A TEACHER
(1) If you insist on using the word "business," you could try this method (which
is firm yet not overly rude):
Mona: I hear that you are dating Tony.
Sue: That's right.
Mona: If I were you, I wouldn't date him. He belongs to religion X, you know.
Sue: (BIG smile) I think that's my business, don't you? (BIG smile)