Ask Mr. Smarty Plants

Well, you may have to learn to like Acalypha phleoides (shrubby copperleaf), or be more aggressive. It is native to this part of the state, and therefore very adapted to the rainfall, climate and soil. Since it is perennial, just pulling it off the root is not going to stop it from coming back up, as you have already pointed out. You can't spray it with herbicide, as it would kill all the other dicots or broad-leaved plants (like the straggler daisy) that you already have. If you buy a spray that is for monocots, or grasses, it won't bother the three-seeded mercury, but it could kill some native grasses that you have been cultivating.

The first thing to do is make sure it never has an opportunity to go to seed. Even though it is a perennial that can come up from the roots, it will also propagate itself by the seeds on those tall bracts. This might be a time to break your rule about never mowing; if you mow it before it can seed, and keep mowing it as it sends up more bracts to try to seed again, you might just wear out the food stored in the roots. Doing this for several weeks when the plant is trying to bloom, and thus set seed, could greatly alleviate your problem. 

Beyond that is the somewhat labor-intensive, hands and knees on the ground, method of painting the cut stem with a wide spectrum herbicide. Begin with a small bottle of the herbicide and some disposable sponge brushes. Cut each stalk off near the root and quickly, within five minutes before the stalk starts to heal over to protect the roots, paint the cut edge with the herbicide. Be very careful, spilling this could contaminate the soil and kill the other plants, broad-leaf and grasses, and don't spray, for the same reason. This plant is monoecious, which means it has both male and female flowers on each plant, and each plant can carry on creating more plants with no outside help. 

From our Native Plant Image Gallery:

Acalypha phleoides

Acalypha phleoides

Acalypha phleoides