How should I clean my slate and stucco outdoor patio area?
If you are not sure about whether a  your paving is capable of withstanding the jet of water from a power washer, test a small hidden area first.

Natural stone and slabs have the highest resistance to power jet water stream. It is not uncommon to see small pieces of stone or slate taken of by the water stream. You should wear glasses because this can ricochet and get lodged in your eyeball ... ouch.

You need to take care with "wet-cast" slabs and paving. 

I would recommend using karchers dirt blaster ...



It has a weird cone shape on the end that actually spins the water at high pressure making the cleaning much more effective.

You should then regulate the distance and angle at your own consideration. 

I usually pull away when cleaning the concrete joints as the water stream can easily rip them out. Then do a quick sweep on the tile and only concentrate on areas where tough stains are left. There have been times where small pieces of stone were forced out of the slab and nearly blinded me -- Wear safety goggles!

There is also patio cleaner that does not spew water and debris all over the place and is a bit safer to use on sensitive material.




  Power-washing is particularly effective at removing mosses and algae
  that seem to thrive on certain types of paving, most notably
  'textured' patio paving and clay brick pavers. We find that the
  addition of Jeyes Fluid tends to inhibit the return of this type of
  vegetation for a short time, whilst not affecting the pavement
  surface. Certain quality sealants are also reputed to inhibit or
  prevent algal growth, but are an expensive way to eliminate a minor
  problem.


You would need to find some local advice on sealants that you can use on the particular slabs you have got. They can work well sometimes -- but also can be a waste of time the rest of times.