Some trees will come back with a vengeance if you just grind them to below grade and cover and do not kill the roots, Locust comes to mind but they're are others. If that is the type of tree you have cutting as close the ground as possible and then drilling a bunch of 1" holes about 12" deep in the stump then pouring Epson Salt and cap with melted wax from a candle. Cover with black plastic and then dirt. This will kill all of the roots and keep the tree from spouting again.
Pine, poplar and most oaks will not spout back from the stump so just cut as close to the ground as you can and if you do not want to grind the stump just cover with dirt and wait until it rots.
