Pine trees have "big, wide, flat root systems," explains landscape contractor Roger Cook of This Old House. After cutting down the pine tree, a sometimes labor intensive chore, you will need to deal with removing its stump and roots. Hand-digging the stump and its roots with a shovel and axe is out for large trees with large roots like pine trees. Use a simpler, less labor intensive, but chemically-based method, for this chore.
Tie a piece of rope around the pine tree's trunk. Make it long enough to provide you with enough length to be able to step away from the tree a few feet, but still be able to keep your hold on the rope. This piece of rope will help you guide the tree when it falls.
Cut the majority of the pine tree down to the ground, cutting it as close to the ground you can. Use a sharp chainsaw and made a V-shaped undercut on one side, that extends to about one-third of the trunk's diameter. Make this cut on the side in the direction of where you want the tree to fall. On the opposite side, make a straight back cut just above, about one-third of the trunk's diameter, where the "v" of the undercut meets. Leave one-third of the trunk's diameter uncut to create a hinge.
Turn off the chainsaw. Step away from the pine tree quickly after you make the cuts, and guide the direction of the fall by pulling it with the rope. Once the tree starts to fall in the chosen direction, head to a safe location out of range of the falling tree.
Drill 1-inch-deep holes with a spade bit into the pine tree's stump, just around its outside perimeter. Space the holes three inches from stump's edge. Drill some additional holes on the sides at 45-degree angles to allow for venting.
Fill each hole with a stump removal chemical. Follow the specific application instructions provided with the stump removal chemical. Reapply as necessary based on the instructions provided.
Break apart the pine tree's stump with an ax once it changes into a spongy texture.