Dish Soap Will Harm Your Grass
The degreasing agents and bleach that is often found in dish soaps are toxic to plants and is designed to destroy the fatty acids and organic matter that is commonly found in food.
Will purple power kill grass?
Ignore the post above me if you are using purple power to clean your concrete yes it will kill your grass. What I would suggest is to soak the grass near where your working and if there is some accidental spill over hose it down as quick as possible to dilute it.
Can I degrease my engine in my driveway?
If you clean the engine on your driveway, it seems that you would be risking an ugly stain. You can't do it in the street without the runoff (illegally) going into the sewer drains and out to the rivers, lakes, or ocean.