Mugwort (Artemisia vulgaris) is a terribly difficult to manage weed and there is no technique or control that has been developed yet that will eradicate it in your yard. It is considered a prohibited invasive species in the states of New York, New Jersey and Connecticut.

The advice of the Invasive Species Management organization for the Lower Hudson Valley and the Cornell Cooperative Extension system is that you can gradually reduce mugwort in a limited area by combining mowing to deprive the plants of their leaves needed to photosynthesize and chemical applications. I am linking here to a summary from the Lower Hudson PRISM of best management practices as well as some details that help to explain why this plant is so difficult to address. It will help with techniques to avoid as well, such as pulling up the plants, which may only make matters worse. Sticking with the repeated treatments is important for maximum impact. 

We are not able to advise you on the use of chemicals in your landscape. For the products that are licensed and effective in your area as well as safe use advise, reach out to the Cooperative Extension Office in your county by phone or email.

Courtesy of NYBG Plant Information Service