They should fall off eventually, although pruning the plant is fine as well. Spider mites don't normally spread disease on mint if that's what you were wondering...

Are you planning on using the plant as a herb?

Agree, they'll die off on their own. Either way, don't let the dead leaves sit on the surface of the soil; they can become ground zero for re-infestation.

Be super careful with that insecticide; it's one of the strongest (and broadest acting) on the market. Make sure you read the application instructions and precautions on the label twice before using. If you want a little less toxic option, spider mites can be controlled with either Neem Oil or Insecticidal Soap treatments.

Mint is really not ideal for growing indoors - it likes full sun, good airflow, and slightly moist but well-draining soil. It would really do better outside. Inside it is prone to mites, which you've had and which will probably come back, aphids, and fungus gnats, not to mention mildew and fungal problems.

We were planning on using it as an herb. Do you think it's dangerous to use it as an herb now that we've sprayed it with that insecticide? We moved him back outside, and plan on only bringing him in if there are strong winds or a torrential downpour. Do you think a couple of light rainstorms would make it safer to use as an herb after having sprayed it with an insecticide?

I don't know. I don't know enough about it, sorry. I guess it depends
on whether the active ingredient functions systemically or whether it
just kills on contact.

Check the label. If it says to reapply
after a certain period, that's probably a good sign. I would wait at
least as long as it says before eating. Also good if the label lists any
fruits or vegetables.

Okay, great. Thanks so much for your help!