While the options for removing a pine tree stump are somewhat similar to the ways of removing other stumps, there is a difference in so far as pine trees have larger, flatter root networks than other trees. The most-effective removal method for a pine tree stump may not be the best removal method for an oak or a spruce stump. Removing a tree stump yourself will save hundreds of dollars, but some methods will require a certain level of physical fitness. As always, use caution when using sharp implements such as axes and handsaws. Patience is key with these tasks, so it's best to not be in a hurry.
If you're working with a small young pine tree stump, simply digging and cutting will probably suffice. Shovel around the stump until you've almost completely uncovered the root system. The roots can be effectively severed with a saw or an axe, but you may find that loppers are easier to use on smaller root systems, given that the uncovered roots are still partially in the ground, and thus not easy to access with a handsaw. Extricate the severed roots and stump from the ground and dispose of them in the trash or by burning.
For larger tree stumps, this same method also largely works, but the tools used and degree of labor involved are different. As with a smaller pine tree stump, the basic goal is to dig around the stump to expose its roots. With a larger stump, there will be a great deal more digging, and using the loppers will not be an option. A sharp, full-fledged axe or handsaw will be needed to sever larger root systems, and you should prepare yourself for a full day (or 2) of chopping. If the tree stump is large and heavy, wrap a chain around the fully severed stump and pull it out by hitching the other end of the chain to a truck. It is important that the stump be completely severed, and that the truck pulls the stump slowly. The driver should take great caution to accelerate the vehicle forward as slowly as possible.
A considerably slower--but equally effective method--for eliminating larger pine tree stumps is to hasten the biodegrading process. Bear in mind that this process may take months. As with the manual removal processes above, reduce the stump to the smallest height possible before hitting the ground. Next, bore many holes of at least 2 inches in depth into the top of the stump. Pour water into the holes, followed by nitrogen-rich fertilizer (the larger the nitrogen content, the better). Douse the area around the stump with the same mixture of water and fertilizer. Cover the stump with damp, organic compost (leaves, wood shavings), and then place a black plastic sheet over the stump, weighting the sheet down so it doesn't blow away. The black plastic absorbs sunlight, heats the compost and the water/nitrogen mixture in the stump holes to initiate the decaying process. This step will have to be redone again and again every few weeks, but it will eventually do the job in an effective, non-toxic fashion.
The last option for removing a tree stump can be dangerous. It is possible to set fire to a stump by building a campfire of sorts on top of the stump. Check with the local fire marshal before doing so. Dousing the stump with gasoline, kerosene or oil is discouraged. Do not use diesel or petroleum products to ignite the stump.