Options to eliminate nutgrass include disposing of the plant and soil surrounding it or use of a sedge-specific herbicide. For heavy infestations, a third option is to embrace the plant and treat it like any other lawn grass.
Technically, nutgrass is nutsedge. Eliminating nutsedge requires understanding its reproductive cycle. If one pulls the leaves of the grass but leaves any of the nuts that grow underground, it reproduces itself from the nuts. In the time it takes for new growth to appear above ground, the plant has further propagated itself by producing more nuts. Some of the nuts are so small that they pass through a sieve unnoticed. However, they are large enough to produce new growth and more nuts.
If nutgrass is just beginning to appear, use a spade to dig a 6-inch circle around each plant. Remove all the soil from the hole and discard it. Do not add the soil to a compost pile or risk contaminating the entire pile. Continue the process until the nutsedge is under control.
If you choose to use a chemical herbicide, choose one that the manufacturer formulates for use on nutsedge. Some manufacturers offer selective herbicides that are safe for use on established lawns and around woody plants.