I know you people don't like certain solutions, but I've found neem oil to be completely useless, a waste of time and money.
Spider mites are only killed effectively by pesticides: generally speaking infestations are treated by using first a broad-spectrum pesticide such as imidacloprid to kill off the adults followed by etoxazole to kill eggs and larvae. Mineral oil can be substituted for the latter, but it is easily washed away by rain and overhead irrigation, so the trend has been for alternatives. Red spider mites in all stages are effectively killed off by dicofol, but this chemical has become harder to find and will surely be banned as soon as Bayer, Suntory, Syngenta etc have a much more expensive alternative to market.
Soap... if we are talking about ordinary household soap it's a "grandmother's remedy", meaning completely useless but still used nonetheless. Potassium-based soap is moderately effective against scale insects but it's mostly used to help fight aphids (blackfly and greenfly) because it's effective to wash away the honeydew they produce which can attract ants and especially provide fertile ground for fungine infections.
