You can get cold or hot pressed Neem Oil. It is an extraction of a from a tree's leaves that stops mites fast. It is the most common non-chemical cure that I am aware of here in Cali. You use it by diluting about a tsp per qrt of water and spray under sides of leaves especially (That's where the eggs are) so you can kill adults and offspring.

Here's more info http://www.greeneem.com/about.htm

What part of the world are you making greener?