While mites are technically arachnids, the pesticides used for them are still typically regarded as "insecticides". That being said, definitely pick the pesticide that will work on JUST what you're trying to kill. Otherwise other beneficial insects (and other creepy crawlies) might be harmed. Basically if it has an exoskeleton an insecticide is what you should go for. Although remember to use one that targets the SPECIFIC insect/arachnid/creepycrawly that you're trying to kill. And keep clear of herbicides.
What a load of nonsense.
insecticide is a poison against insects. Mites are not insects.
For mites you use miticides
www.britannica.com/technology/miticide :
Miticide, also called Acaricide, any chemical substance used to control mites or ticks (especially species that damage ornamental or food plants), which are not susceptible to commonly used insecticides.
If you want a generic name for stuff that kills pests, its called pesticide.
Do not try to blur the lines. It does NOT help the OP.
I was very clear, stating that the OP needs to verify the package explicitly mentions mites, as insecticides are not made to kill mites. In general, spiders are very usefull to have.