Mites don't eat soil, they survive on plants. However, the requirements for survival of spider mites is very low: they do just fine for weeks (perhaps longer) without sustenance. Wiping them all out can be difficult.

Bonide Mite-X claims to get rid of mites, and is comprised of "botanicals" such as "Cottonseed Oil, Clove Oil, Garlic Extract And Other Botanical Extracts" and is therefore less likely to harm people and pets.