Neem oil stops bugs from shedding their shell while they grow. Thus they are never allowed to mature and reproduce. So after a few weeks they should pretty much all be died or close to it. You just got to keep spraying your plants every 3-5 days with it.
I've used hardcore mitecides before as well and honestly neem oil works just as good or better and its organic. I'd only use a mitecide if you're in veg as most of them can take 60 days or even longer to leave the plant. You can use neem oil up until the last two weeks with no negative effects.
The best solution is to stop mites before they go crazy. Keep a clean environment and don't under water your plants. Mites like it dry and will reproduce faster in a warm dry environment.
I personally use
http://www.entomo419.com neem oil because its turned into micro particles and will mix with water without adding any type of dispersant.