Spidermites do survive outside quite well unfortunately. It can be a big problem for herb gardening. (I have a large medicinal herb garden out back, no weed growing yet though).

Spraying with water can help but like one poster said, the water can burn them. You can try spraying in the early morning hours so there's time for it to evaporate before it gets hot. I wouldn't do it at night though as you can run into mold issues.

You can also try buying some live ladybugs. They're sold over the internet. If you release them into your patch they can and will devour those mites along with the eggs. Beneficial nematodes are great for soil bugs. But the spider mites are preyed upon by ladybugs. And hopefully, if you're lucky the ladybugs will stick around and lay eggs for you. The ladybug larvae are the ones that eat the most. They look like tiny little alligators, so dont kill them if you see them, those are good

Good luck!

Sabrina