There's an organic product made specifically for mites. It's called Liquid Ladybug. I haven't used it but I've heard that it works. For orchids that are not in bright sunlight, horticultural oil works very well. The one I use is called Organicide but there are others and they all work equally well. Be careful where you spray oil products because they're difficult to clean off and they will stain many surfaces. Orchids with oil on them will burn if put in bright light. I also like insecticide soap for most insects but I've never used it on mites. The process that Dr. Martin Motes talks about in his book "Florida Orchid Growing" is to use a horticultural oil first and then an insecticide soap a week later. No matter what product you use, you need to treat the plants at least twice, a week to 10 days apart. That's to kill any newly hatching eggs. Some growers say to treat a minimum of three times. Be sure to spray the underside of all leaves.