Spider mites usually become problems during hot, dry, weather so misting of affected plants is a good first step toward control. Sharp sprays of water that dislodge the wee buggers is also a good control method. For more persistent infestations Insecticidal Soaps, superior horticultural oils, or maybe a Neem Oil product may help.

http://homeguides.sfgate.com/basil-plant-mites-38804.html

kimmq is kimmsr

Horticultural oils are mostly petroleum based, not an organic solution, and I would be reluctant to eat leaves with petroleum residues on them, no matter how refined they are. They will also kill the beneficials and predators too.

Neem oil is only trivially toxic to humans (don't drink a glass full) and on plants it has a smothering as well as a toxic mechanism in its pest control. The smothering but can work on spider mites, which, being penetrating suckers, aren't affected by the toxicity of the oil. It is claimed, in places, to be repellent also.

They say watering stress and extremely dusty conditions exacerbate spider mite infestations, as does overuse of horticultural oils by clobbering their enemies. Detergent-y water wand/spray would be my suggestion.

I would throw it out and start over again.

I use Safer insecticidal soap link Use late in the evening to avoid wet leaves scalded by the sun . You'll probably need to repeat it every few days until the spider mites get under control. But this stuff can be used up to the day of harvest - its based on potassium salts or something.