--How in the world did you persuade her?
--Never you mind. (=I'm not going to tell you.)
Can we use 'Never mind' as a response in this context, with the same meaning? Thank you in advance.
Yes, you can.
Rover
With respect to Rover, I'd like to expand a bit. In AE, never mind is used to assure someone that whatever they were asking about is of no importance and not worth further inquirey. "What did you say?" "Never mind, I was just thinking out loud."
Never you mind is used to tell someone that what they were asking about is none of their business, as in your example. It's a fine point, and there certainly is some overlap.