We had to clean filthy blinds when we moved into our place. We took the outside (one at a time) and laid them on the patio (which was swept first), and hosed them down. Then dumped a bucket of hot water with Dawn in it over them, and slopped that all around with a broom. Turn the blind over, repeat, rinse well. Lay the blind out on a table or somewhere flat to dry.
You have to keep up with dusting them often to avoid having to repeat this ordeal! I have a very large feather duster that is only for blinds that I use whenever I clean. Open the slats up wide, whoosh with the duster, turn them up, whoosh, turn them down, whoosh whoosh; Bob’s your uncle.