It's not feasible for everyone, but as a form of biological control, animal grazing is an effective method of dealing with invasive weeds as long as it's done properly. Sheep, goats, and cattle are common grazers that will eat most weeds. However, keep in mind certain weeds/plants are toxic to certain breeds of animals. Sheep can typically graze on kudzu, thistle, wild parsnip, garlic mustard, and knapweed (to name a few), while goats can graze on those weeds in addition to black locust, crown vetch, honeysuckle, multiflora rose, and Japanese barberry. Cattle can graze on knotweed, wild parsnip, kudzu, and thistle (to name a few). Grazing may be needed for multiple consecutive years, sometimes multiple treatments per year.
Cutting or Mowing
Cutting, tilling, and mowing are mechanical control techniques most effective on large areas infested with invasive weeds. This method works best when done several times during the weeds' growing season, just before the plants flower. However, avoid cutting or mowing invasive weeds after the seeds have developed as this will cause the seeds to spread and form new weeds. Although cutting or mowing repeatedly does weaken the population of invasive weeds by depleting their root reserves, this method works best when combined with other control methods such as organic herbicides or mulching.
Mulching works best after you've already mowed, cut, or tilled the invasive weeds. It doesn't matter the type of mulch you use as long as you keep the ground cover for at least one growing season. The goal is to smother the plants' stems and prevent any sunlight exposure, which will prevent new growth and ultimately cause the plants to die. Black plastic, carpet, and other impenetrable barriers also work well.
Organic herbicides are become more prevalent because they're highly effective, yet harmless to surrounding plants and trees. They typically work by burning off the waxy cuticle that guards the weeds' cells against water loss, producing nearly immediate results. Unlike traditional herbicides, organic herbicides only kill plants that get their foliage directly exposed to the treatments. WeedPharm and Blackberry and Brush Block are two extremely effective organic herbicides that use super-concentrated vinegar and other safe acids to kill invasive weeds. Normal household vinegar won't kill mature weeds, but it will take care of baby sproutlets.
Digging or Hand-pulling
If you don't mind engaging in some old-fashioned hard work, get out your gloves, hoe, and shovel and start manually removing those weeds. As you can imagine, manual control is the most labor-intensive method of dealing with invasive weeds. Whether it's effective depends on your ability to eradicate the entire root of a weed to prevent resprouting. The manual control technique works best in loose, sandy soil or ground dampened with water, and this technique is not economically feasible on large weed populations or pervasive infestations.
North Coast Gardening
Wisconsin Department of Natural Resources