Remove the wisteria in your landscape as soon as possible. Ideally, a wisteria should be dug up when it is still a young plant. Mature wisterias have extensive root systems that will be difficult to remove completely.
Cut the wisteria down to the ground. It will be much easier to dig the roots out if the plant is out of the way. A saw may be necessary for the thick, lower branches.
Dig the roots out using a spade or pick to cut through the roots. Get as much as possible, but note that wisteria roots can run deep and under the garden, grass and other areas, so getting it all will be near impossible.