Red slime is also called cyanobacteria and it is caused my excess nutrients in your water. Do a few PWC and increase flow in the affected areas if possible( dont blast a softie with direct flow).
You can also siphon it out with airline tubing, but it will just come back until you fix the underlying issue(nutrient saturation).
As far as it being on your coral, just get a turkey baster and blow it off, cyano is soft.