Stumps can be removed using a chemical method, or a physical method.  The chemical method involves "rotting out" the stump, while the physical method requires chipping out  the stump with a stump grinder.

The Chemical Method

    A stump will naturally decompose with time.  However, several things can facilitate the process. 
    Drilling holes across the growth rings will allow air and moisture to penetrate the stump.  Adding nitrogen fertilizer to the holes will further hasten the natural process of chemical decomposition.

    Several chemical products on the market can also be added to the holes, and after a specified amount of time, the stump can be burned out.   Check with your local garden center for the products available in your area. Be sure to read the instructions for applying the chemical to your stump.
Although these products are effective, they may take several weeks to work.

The Physical Method

    A faster method of stump removal is to chip it out.  A stump grinder is a machine equipped with a wheel of sharp carbide teeth.  The wheel rotates at a high rate of speed and chips the stump into sawdust.
    Stump grinders can be rented at your local rental shop.  Check with your neighbors to see if they too have a stump problem.  Sharing rental costs is a good way to keep your costs down.
    Models of stump grinders may vary.  Ask your rental agent to demonstrate the proper method of operation for the model you rent.  The following are a few things to remember when grinding your stump:


-    Be sure to clear the area of people and pets.  The grinder will throw debris in a circular pattern.
-    Wear ear and eye protection.
-    Turn engine off to reposition.
Great Outdoors Internet Treatment for segment     #5717- Stump Removal

-    After grinding the stump, it is important to immediately remove the sawdust 
     from your lawn.  This will prevent the sawdust from burning the grass   
     underneath.
-  Fill in the hole with good top soil and plant the bare spot.