Mind Your Own Beeswax

Most likely nothing more than a jokey, rhyming stand-in for "business," probably chosen specifically because it sounds less harsh than telling someone off directly. The word "beeswax" is documented as 1930s American slang. One etymologist, Mark Forsyth, has pointed out that "beeswax" was also 19th-century slang for a tedious bore, raising the possibility the phrase originally meant something closer to "mind your own business, you bore." A popular story claiming women with smallpox scars used beeswax to smooth their skin, and snapped at anyone who stared, is well travelled but has no evidence behind it.