Ask Mr. Smarty Plants

From the Texas Sheep and Goat Raisers Association Learning About Goats: (read the entire link)

"Because goats will eat just about any type of vegetation, they are increasingly being used to control unwanted vegetation. Leafy spurge, an exotic species of weed poisonous to many types of animals, is taking over range land in many parts of the western United States. Tall whitetop, also known as perennial pepperweed, is another invasive plant goats are being used to help control. In Texas, landowners are using goats to control brush, particularly cedar. Cedar re-growth in fields crowds out native grasses and depletes the groundwater supply. Current research has even determined that certain goats have a genetic preference for cedar. Goats help to control this re-growth and enhance the amount of water percolating into the ground. By using goats to eat these invasive plants, landowners are helping the environment by removing the plants that are crowding out beneficial species. In addition, they do not have to use herbicides to kill the plants."

We would really hope you would not completely remove the Muhlenbergia lindheimeri (Lindheimer's muhly) (read the entire link). It is an excellent grass, endemic to the Edward's Plateau, foraged by cattle and other animals, including goats, useful as a small wildlife cover, does not need to be trimmed back in the winter, and helps to shade out invasive weeds. We don't recommend herbicides anywhere that livestock will be feeding; it can spread and kill things you didn't want killed.

If you are determined to eliminate a useful plant, pulling it out of the ground and not permitting it to set seed is about the only alternative.