Georgia It all depends on the type, number and size of the stumps. Some trees have big, wide, flat root systems, such as pine trees. Some trees, like oak, have deep roots and a tap root that goes straight down, which makes digging extremely tough. Digging by hand works best for small, shallow-rooted trees.
Essential tools are a shovel, an axe or grub hoe with axe head, loppers, and a root saw.
The trick is to dig and expose roots, then cut with the appropriate tool, pull the roots out of the ground with the grub hoe and put them in the compost pile. I remove all the grindings to the compost pile and fill the craters with loam. If you enjoy running such equipment, these machines are available at rental houses. If you have many stumps to get rid of, a stump grinder is the most economical way to go. Make sure you get complete instructions on how to operate the machinery and wear appropriate safety equipment.