How can I get rid of miniature morning glory ground cover.

Cover with cardboard or 9-15 sheets of newspaper starting a back of area til you work yourself out of area, then cover with 2-3 inches of mulch then use Preen on mulch. Plants have to have sun, soil and water to grow. If you can't get rid of two of these then block out the sun.

See if you can find people who want them more than you do and let them dig them up and take them to their house and plant them.

This is actually a weed that mimics morning glory. KNowing that helps to just rip them out, turn over the dirt, then cover with cardboard or newspaper for a while. I don't use chemicals, because they do affect the dirt and future plants.