Yes, where we have yard type grass, it's either Centipede, or Bermuda, and does get cut low.

The only thing that I know will effectively kill plants through the roots, is Imprazar. It's first common names were Powerline, and Arsenal. Power companies sprayed it under powerlines (probably still do, although I see they must be mixing it with something to kill Pines now in the same spray), and Arsenal was used on new stands of Pine timber to kill Sweet Gum. It won't kill a Pine tree, and I'm not sure about other evergreens, but it will kill about everything else. It doesn't take much either.

Weeds like Wisteria, or Johnson Grass are spot sprayed. It does leave a little dead spot, depending on how you have the spot sprayer adjusted, but Bermuda will fill it back in next year.

Sometimes a Sweet Gum will come back the next year, but the leaves will be tiny. Hit again, any time in the growing season, and it won't come back the next year.