It's as if the speaker began to say "mind your own business!" then changed the last word. It's slightly slangy, and less direct.

It means to stop trying to pry into ones private affairs or do your own work stop annoying me :)

Be busy with your work.

It is just this slang habit of changing some words by using their first letters and modifying the rest for sounding more polite or not using sometimes an embarrassing or slightly improper term. In this case 'beeswax' is a substitute for 'business' ,where business isn't a bad word to use,,but the whole expression sounds a bit rude, therefore another similarly sounding word will be less direct and might sound neater.