You may not like this approach but we cut them off level with the dirt and then let them rot. You can run mower over them. We do have a tractor with blade but it is impossible to pull out until the roots break down. Then you can tilt blade and hook it under the edge of stump and then pop clutch on tractor and they will pop out of ground.
Your other choice is to dig all around stump and cut off under surface but that is too much work. Using axe is far to much work.
Robert D Bard

To speed up the decomposition of the stump, you can drill holes in the stump and fill with molasses.