Remove the newly sprouted plants in the spring when they first emerge from the soil. Use a plant trowel to dig up each bulb. If desired plants grow nearby, use care, because grape hyacinth bulbs may naturalize very close to other plants, and you may disrupt other plants as you attempt to dig up the hyacinths.
Monitor the growing area over the summer, and remove any surviving grape hyacinths to prevent blossoming. If you allow the grape hyacinths to blossom, they may drop seeds over the soil.
Apply a nonselective herbicide such as glyphosate to the plants in late summer or early autumn. Spray the plants on a sunny day when the temperature is between 60 and 80 degrees Fahrenheit. Apply glyphosate to the plants while they still are actively growing, so the herbicide will travel throughout the hyacinth foliage and roots.
Continue to remove plants as they appear in subsequent growing seasons, using both the digging and herbicide methods to get rid of the grape hyacinths completely.