Tree stumps and roots can take a long time to decompose naturally, often more than 10 years. However, there are ways to speed up the process. One way is to allow shoots that grow from the stump to reach approximately 1 foot in height before cutting them off. This will deplete the resources of the roots quickly, causing them to break down faster.
Another option is to treat the leaves on the shoots with a herbicide. The poison from the herbicide will be absorbed by the leaves and will travel to the roots, killing them in about a year. Painting the very stump of the freshly cut tree with herbicide also helps kill roots. Drilling some holes in the trunk and pouring herbicide inside can also help speed up the process.
It can take two to seven years for the constant removal of sprouts from stumps to completely deplete the nutrients stored in the roots. If left untouched, a tree's stump and roots will begin to rot and, over time, become a home for pests, fungi and other organisms. Copper sulfate is a natural herbicide and will kill small tree roots that invade sewer pipes. Cutting off root shoots and saplings that try to keep the tree growing is also important.
Soaking leaves thoroughly in white vinegar can help destroy tree roots as well. Do not remove roots that are close to the trunk or that are fused with it, as they are fundamental to the structure of the tree.