It will, but the mites may build a tolerance to it over time. They're adaptive little bastards.
I use an alternating cycle of neem, einstein and a product called SMC (spider mite control). The SMC is organic ( i don't know why i didn't mention it in my prior post...had a stoner moment). Ingredients are: 1% coriander oil, 94% Canola oil, and 5% triethanolamine
But.... even with me alternating products, i seem to have contracted mites that just will not die right now.
To kill them for good,
Floramite is the way to go, but it is in no way organic.