how to get rid of mugwort

please help has ruined my garden , it will get 10 feet tall ihave tried roundup , burning it, digging it,no luck on those please help

I don't know specifically about mugwort, but basically to get rid of any plant, you must kill the roots. You can poison them (Roundup) or starve them (cut more or less continuously, or smother the leaves from the sun) but until the roots have no more energy left they will continue to send up shoots. The Roundup might work if you use if more than once, on the subsequent attempts to send up shoots after the first fight. You're getting rid of the leaves (and root tissue) so they can't send more energy down to the roots. Eventually the Roundup should get rid of all the root tissue too.

I had wall to wall mugwort in my backyard. Tried Roundup many many times. Finally I tried Lontrel. Prayed carefully on the leaves. Formerly only available for professionals but now available through Amazon. It is expensive. You do not need much but the smallest size is 1 quart. When I started planted again the following year I saw the roots of mugwort. They were black! Now fighting bindweeds and Bermuda grass!