Mondo grass (Ophiopogon japonicus) is colloquially known as "monkey grass." It is an evergreen perennial that grows to heights of 8 to 16 inches. Mondo grass is hardy and spreads quickly, which makes it an excellent choice for a ground cover. This is especially true in areas where other plants fail to thrive, such as shady spots under tall trees. Gardeners who introduce this ornamental grass into their yards appreciate the ease of propagation, which requires little more than dividing larger plant clumps. Therein also lays the problem when trying to kill it--it is supremely hardy.
Mow the monkey grass on the shortest setting. Repeat this step whenever new growth appears. Scalp the plants frequently and discourage the formation of stolons.
Dig down 12 to 18 inches deep with your spade around the area perimeter. Install a root barrier around the outer limits of the area containing Mondo grass.
Dig up clumps of Mondo grass with the spade. Separate as many of the plants' rhizomes, stolons and roots as possible. Carefully rake up all of these pieces and discard.
Cover the treated area with the tarp. Weigh down the tarp with rocks. Keep the tarp in place for a few months.
Remove the tarp and dig up any dead plants with the spade. Dig about 12 inches down to unearth dormant rhizomes. Discard all plant pieces.