Killing any vegetation without an herbicide means you can either hand pull each grass clump and all roots or smother the life out of all the plants in the mound by denying any sunlight from hitting the plants for 6 to 12 months. A covering of cardboard or newspaper with three to four inches of wood chips on top or even layers of old carpet or plastic that can keep out all sunlight will starve the grass and the grass roots - all plants need light to survive. You can try a hybrid of this by clearing the soil of weeds in just a small area then putting down strips of carpet or newspaper and mulch as pathways. Plant in the narrow rows and keep them clear of weeds. In a cool climate you can cover the bed with black plastic, make slits in the plastic to add your veggie seeds and plant starts and let the food crops grow in the slits while the black plastic keeps the weeds down. In a very hot climate the plastic may not be practical. Good luck and stick with it to win your war with weeds. Keep growing, Marianne Binetti