STUMP REMOVAL
By Hand
One way is to cut the tree down as low to the ground as you can safely do that with a tree saw or chain saw. Once you get the tree cut down, you will need to dig the soil around the tree roots and expose as much of the roots as you possibly can.
With a sharp axe you should be able to chop the main roots all around the tree. Once you chop out the main roots you can try to dig under the stump and get a heavy duty chain around the tree stump by using a pry bar to loosen the stump and roots. Keep the bar at such an angle that eventually you will be able to get to the centre of the stump from underneath with the tip of the landscape bar.
Once you get the stump loose enough, you could attach a truck or tractor to the chain and pull the stump out of the ground. Just keep doing this all around the stump. At first it won't seem like you're getting anywhere, but eventually you will see the stump start to move. Manual tree stump removal is cheap but has the drawback of being labor-intensive.
For large tree stump removal, taproots may be imposing enough to require cutting with a full-size axe. If hand removal is considered, the trunk of the tree should be left as tall as possible, to provide leverage to loosen and break the roots as the digging progresses and so that when you pull the stump with a tractor or truck it will have more grip on the tree for pulling.
Tools you need to remove a tree stump by hand:
* Round Mouth Shovel
* Sharp Chain Saw or Tree Saw
* Heavy duty sharp Axe
* Pry Bar for prying the roots loose from the surrounding ground
* Heavy Duty Chain
* Truck or Tractor
Chemical removal
There are several chemicals available at garden centres that will hasten the rotting of a tree stump. This basically involves drilling a series of holes in the stump and adding the chemicals. While this method definitely does speed up decomposition time, don't expect it to be lightning-fast. The stump will still take a prolonged period of time to break down.