Question
I cut the stump as close to the ground as I can, cut slits in it, with the saw, & pour in/on table salt.  It works.

Answer
The salt will kill the root system and stop the tree from sprouting but will do little fo the rotting of the stump infact depending on how much salt was used it may make the area strile for awhile. I would check with your local garden type store for a product that can be poured on in the holes in the stump and will speed up the rotting. One of these is simply called Stunp Rot.