i don't recall the name of the other common pest that causes similar leaf damage to mites, but if i do remember correctly, it was a similar treatment to get rid of them.
a good neem oil treatment in a 3-5-7 day cycle on any plant showing symptoms. hit them once to kill the living mites, then in 3, 5 and 7 days later to kill any new ones as eggs hatch.
also a good idea just to use it preventively on plants that don't even show symptoms. i always neem after transplanting or when starting flower (and once after that a few days later) even if the plants show no signs of an infection or symptoms. it's just good practice.
there is no eradicating mites or other creatures, that is a futile chore. all you can do is prevent with clean, suitable conditions and mitigate with safe pest control measures.