Best way to get rid of this section of lawn?

I want to lay a stepping stone path (marked out by the bricks) and replace the grass with something a bit easier to maintain between the stones, like kidneyweed or something similar.

Only problem is my soil is clay it’s proving quite difficult to remove the grass. Also I’m worried about not quite getting it all and the grass growing back after I’ve done everything.

How is something like this usually done and what would be practical in this situation?