Invasive Ground Cover
You may use ground cover plants to fill your garden and backyard to fill the bare space and suppress the growth of weeds. However, their invasive characteristics make it hard for other plants to survive. Some native ground cover plants should be chosen to avoid inference with the growth of other plants. If you want to remove one species of ground cover plants in your garden, you should use the herbicide carefully because other plants may also be affected by those chemicals.
Before the real removing work, you should use some tools like shears to cut the plants on the ground instead of in the air to avoid leaving seeds for the next year. Carelessly mowing may also spread the seeds into another area. Then you should collect the sheared plants together and put them into a container specially designed for plants to avoid the further spreading of their seeds.
Then you should dig out the roots of the invasive plant using a hoe and get rid of it with the leaves together. You should thoroughly clean the soil to avoid any further growth in the next year. You only need some patience to do this work since you should carefully collect all pieces of plant parts to clean them completely. After that, some spray herbicide can be applied to the soil to kill the remaining seeds in soil if you have no plan to plant other plants in this area. If you see some new seedlings of the invasive ground cover in the next growing season, eradicate them immediately. You should do some cleaning frequently to get rid of them completely.
Image provided By Libby norman (Own work) [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons