Sprinkle granular pre-emergent herbicide over the soil surface in the spring as perennial plants begin growing again. Apply the herbicide in a thin layer over the soil everywhere you have seen goat head plant growing in previous years. Water the soil thoroughly after applying the pre-emergent herbicide.
Dig up goat head plants you find growing in your landscape. Insert the blade of the shovel as deep as possible into the soil to remove the entire taproot of the plant. Place the plant into the trash bag to dispose of it. Check the soil surface around the location where you dug up the goat head, looking for burrs that may remain on the soil surface. Pick these seeds up manually with your fingers and discard them in the bag. If you leave seeds on the soil surface, they will eventually germinate to create new goat head plants.
Spray a post-emergent herbicide spray onto goat head plants that continue to thrive in your landscape. Saturate the foliage of the plant thoroughly, being careful not to spray nearby desired plants with the herbicide. Wait for up to two weeks for the herbicide to begin killing the goat head plants. If the plant continues to grow after this time, apply the herbicide a second time.