Permethrin and pyrethrin kill mites dead. I’ve been using it for years.
The key to effectiveness is the interval of repetition; it has to be shorter than their reproductive life cycle, hence the name of the strategy; “life cycle interruption”.
Once or twice won’t cut it. The mites are too small and some will inevitably be missed the first or second time through. That’s why I recommend doing it at least 4 times.
The downside is that it will kill all your beneficials as well.