Sometimes you may find that you need to remove a bush from your landscaping. Cutting it down is not usually a problem as much as what to do with the remaining stump. Several methods are available, but the simplest approach may be the best.
Pull back any brush that is on the ground and the mulch that might be around the stump. Use a garden rake or your hands, depending on the size of the stump being removed and the amound of material on the ground.
Start digging about 6 inches back from the base of the stump, and remove the dirt from around the old bush. Dig in a circle all around the bush, setting the dirt aside to be used later to fill in the hole.
Cut any roots you encounter, using a reciprocating saw and inexpensive blades. (Use inexpensive blades because you will hit dirt as you saw through the roots, and it will dull the blade very quickly.) Change the blade as soon as it becomes too dull to cut efficiently.
Dig down about 8 inches, cutting the roots as you go and removing the dirt until you just have the base of the bush stump showing. Use the reciprocating saw to cut through the stump, perpendicular to the ground. Don't worry about getting a straight cut, since it will be buried.
Apply a heavy coating of herbicide to the top of the stump if you are dealing with an aggressively growing bush as it may force up new shoots, even after being cut away. Refill the hole, adding a little dirt more as necessary to level the ground and tamping the dirt as you go. The remaining roots should rot away over the next months and years.