Spider mites come in hundreds of varieties and feed on as many varieties of plants. The damage they do is generally insignificant but if populations are allowed to get out of control, severe damage or death can occur. There are a number of ways to control spider mites but using white vinegar is not among the recommended methods.
Spider Mite Damage
Spider mites feed on the cellular tissue of plants. They leave white or tan spots on leaves. Some produce webbing. The damage is generally insignificant unless populations become excessive.
Good plant maintenance helps prevent spider mites. Once they are present, a simple rinse with a powerful stream of water can remove most of the pests. Horticultural oils or soaps are another option for dealing with spider mites. Pesticides can eliminate the biological enemies of spider mites and allow the population to increase rather than decrease.
White vinegar is acidic in its makeup and would likely kill spider mites. However, it is not recommended and its acidic nature maybe harmful to delicate plants.