Rinsing them with a strong water spray will help tremendously.

Using an insecticidal soap is better- not dish soap but real insecticidal soap. Some dish soaps might work if they are the right type soap and not a detergent, but that's a crap shoot. Real insecticidal soap is cheap and stores really well so keeping some on hand is a good idea. Neem oil will work, too.

Whatever path you take you will need to repeat it a couple of times a week for a month or two as eggs are always hatching.

Then going forward either increase your indoor humidity or get into the habit of rinsing plants off in the shower periodically- spider mites thrive in low humidity/dry conditions.

first.. get the worst ones out of the house.. isolate them ... if they arent rare or beloved.. maybe just get rid of them ...

most dish soaps are detergent .. and therein lies the issue ... since you dont say what kind.. its hard to opine ...

how about a pic or two.. so we can confirm your issue ...

ken