Vacuum the sofa. Use a standard bag vacuum, not a bagless sweeper, and vacuum the entire couch, including under the cushions. Use your vacuum attachments to get into the nooks and crannies of your sofa to ensure that as few mites as possible escape your sweep. After you finish, remove the bag and dispose of it.
Steam clean the upholstery starting from the bottom. Use a steam cleaner with attachments intended for upholstery cleaning. By starting from the bottom and moving to the top, you prevent mites from escaping onto your carpet.
Spray the sofa with disinfectant. Use a hospital-grade disinfectant approved for use on fabric. Spray, again starting from the bottom, taking care to hit all parts of the sofa.
Cover the sofa with plastic. Purchase a plastic cover sized for your couch. Seek one that seals around the sofa to prevent mites on the sofa from getting out and those that may be in the environment outside the sofa from getting on.
Remove the plastic after two weeks. By this time, mites on the sofa will likely have died.
Vacuum the sofa from top to bottom again. Dispose of the vacuum cleaner bag just as you did the first time.
Spray the sofa with a final round of disinfectant spray, coating the entire sofa again. Allow the sofa to dry, then proceed with using it as you did before the infestation.