Dig a trench 6 inches away from the base of the shrub and 6 inches deep, with a spade. Water the area to expose the roots.
Press a landscape bar underneath the root system. Push down on the landscape bar to push roots through the soil. Lay the root system on its side.
Cut any stubborn roots with bypass shears or a saw. Chop the root system with a hatchet. Inspect the pieces of roots to ensure the shrub has not suffered from a disease such as root rot, which can spread to other plants.
Place the pieces of shrub in the compost, in a 6-inch layer. Cover root debris with "green" composting materials such as grass clippings in a 3-inch layer over the roots or "brown" composting material. Continue to layer the composting materials until you have run out of root debris.
Water the compost, so that it is moist. Mix up the compost every three to four days to speed up the decomposition process. Use the mulch when the shrub's roots have broken down and created a fine brown organic material.
Cover the stump and root system with 6 inches of dirt.
Water the dirt on top of the stump and roots, to accelerate the decomposition process.
Check the dirt-covered stump area in six months. Press a shovel into the pile to check on the progress of the decomposing roots. Replace the dirt, if the roots have not decomposed in the dirt pile. Then check again, six months later.