I recently weed whacked some tall weeds and grasses around the shop then sprayed with Round-Up. It did not kill some of the grasses that had been cut to about 3 inches tall. I suspect because there was not much, if any, green leaves showing to be sprayed. A second application will be needed once it grows some more foliage.

I would spray first then cut/mulch later so long as you are talking about weeds and such that are under a foot tall or so.

Ground sterilizers would be good to check into as well. Just be cautious that some of them can "run-off" after a rain and kill greenery down hill from the application.

Fish on!,
Noel