Experts and BHG readers answer.
REMOVING WELL ESTABLISHED GRASS
Thanks for writing. The best way to get rid of your grass is to borrow or rent a sod cutter and manually remove the grass. (Sod cutters come in gas-powered and human-powered versions.) You'll remove the majority of the grass crowns, which should keep it from coming back.
Alternatively, an old-fashioned method is to cover the area with a 6-sheet-thick layer of wet newspaper, then cover that with a layer of compost, then spread your pumice over that. The newspaper/compost should kill the grass.
I wouldn't expect the pumice to help with drainage --- drainage problems often are soil or slope related.
---Justin, Senior Garden Editor, BHG.com