In my case I have such blinds on a balcony looking over a big boulevard so they get dirty quite fast. The way I clean them is the following - I take down the blinds when fully extended and closed . After that I take them to the bathroom and I use my shower. My shower is with flexible hose like so that helps.
Now after you pour some water to the blinds they stick to either the floor or the walls. In case the blinds are short enough I use the wall otherwise I use the floor. Use strong flow of water and hit the blinds from one side to the other. The dust literally flows out. You may have to use some towel if the blinds are really dusty or muddy. Cleaning the blinds using this approach is much easier but it is still a challenge for my apartment as I have about 20.
NOTE: remember to remove the plastic part for turning the blinds otherwise it will constantly get in you way. Now I also remove the small plastic part at the end of the strap for lifting the blinds(after I stepped on a few and broke them :)