What will clean concrete and not kill grass?

A pressure washer will definitely kill grass if you don't control where the nozzle is aimed. Otherwise, it will do an Excellent job of cleaning concrete with tap water.

If you need to get a little more aggressive to remove oil and grease spots, try scrubbing the spots with trisodium phosphate (TSP) which is available at most hardware stores. A little TSP goes a long way and the worst it will do to the grass is to make it grow faster because it supplies phosphate, a plant nutrient. Excess fertilizer will, of course 'burn out' grass but you won't likely be using anywhere near that much TSP where you need to worry about that problem. Follow the instructions on the container. TSP strips the oils from your skin and causes instant dishwater hands so wear gloves and eye protection.

There are other surfactants like "Clean & Simple" (from the link below) that you can use, too. I use Clean & Simple to wash everything from Windows to the dog...it de-stinks the dog and kills the fleas. It is non-toxic--being a good surfactant, it simply breaks the surface tension of the water and drowns 'em.