"Do you mind" is used when we are making direct requests. For instance...
"Do you mind if I sat down here?"
"Do you mind if we watched the game instead?"
"Do you mind leaving the room for a moment?"
"Don't you mind" is used when we want to know how someone would feel and/or respond in a hypothetical situation that may or may not have happened before or could happen. For instance...
"Don't you mind when you're complimented for your looks?"
"Don't you mind every time your boss makes a request?"
"Don't you mind when your neighbor's child walks into your yard?"
I hope this helps answer your question. If not, please let me know.