First off I would not do this if you are deep into your flowering cycle and have buds growing. If you are just in veg cycle though these are great and it is good to get rid of these mites before you get to flowering and your options are limited.
If you can seal up your grow area (plants & lights), you should get these Hot Shot No-Pest strips, they are great for spider mites:
The problem with poison sprays or homemade recipie sprays is that they don't kill the mite eggs, so you have to keep re-applying them and hope that it gets into the tiny cracks of the plant since most sprays only kill adults on contact. These No-Pest strips use Dichlorvos which is slowly released into the air from the strip which you just hang or set in with your plants. The area needs to be sealed or very low ventilation so that the poison can build up to a useful amount and kill mites. When new mites hatch out of eggs, they try to breathe the air and very quickly die. Since it is in the air, you don't have to worry about eggs in hard-to-spray areas of the plant, plus it also cleans off any lights/equipment/pots,etc. that you place in the room with the poison. It also takes care of a lot of other bugs, not just spider mites, so you'll clean your plant of any other pests it may have. It will kill beneficial insects too, so don't release a bunch of ladybugs or something and then use this.
Of course you will need to open the area to check on your plants and to water but for the most part it should be fairly well sealed. Use the strips for 2 weeks to make sure all the eggs that are on your plant have a chance to hatch and die before the poison is stopped. While the plants are being treated make sure you clean everything else that is not in with the poison REALLY well. After the poison is stopped, don't introduce anything into your grow room that you are unsure about. Wash your hands and wear clean clothes when you work on your plants to prevent re-infecting them. When the plants are don'e with treatmet, rinse them off really good with water to remove any residue (then place in the dark for an hour or so to let the water evaporate before you put them under the bright lights), make sure you don't re-infect them, and you should be good to go!
Also, you say these are red spider mites? I know they can come in all sorts of colors, but have you seen any damage on your plant that looks like they caused it? I would hate for you to use poisons on your plants when they were some kind of mite that does not do any harm!
