Apply a weed and grass killer directly to the unwanted vegetation. Choose a postemergence, nonselective herbicide. Pre-emergence herbicides kill the grass and weeds before they begin growing, while postemergence herbicides kills the grass and weeds after they germinate. Nonselective herbicides kill all vegetation it contacts, while selective herbicides target specific weeds but do little to no damage to grass.
Cover the unwanted grass with black landscaping plastic. Placing bricks along the plastic’s edge keeps it in place. As the sun beats down on the black plastic, the temperature under the plastic rises and burns the grass, as well as keeping water, oxygen and light away from the grass. This takes several weeks, but it kills the grass without chemicals.
Remove the unwanted sod with a flat shovel. Dig several inches into the ground and lift the grass up. Place the unwanted grass inside a garbage bag for disposal.
Use a mechanical tiller on the top 6 inches of the soil. The tiller turns the top 6 inches of soil as well as grass and dead weeds under and brings the healthier soil to the top. Soil tillers are available to rent at home improvement stores and tool rental centers.