Now that you have successfully removed the tree from your property, what about the stump? You can try to wait it out, but it can take years for a tree stump to decompose on its own. You could hire a professional, but the service can cost hundreds of dollars. Luckily, there are many relatively easy ways to remove tree stumps yourself. The method that you choose is largely up to you and the amount of time, energy and money you're willing to give to the project.
Help nature take its course with a nitrogen fertilizer. Drill many, deep holes into the stump and fill them with the fertilizer. Next, water the stump and the surrounding soil. Then cover the stump with a tarp and cover the tarp with two to three inches of mulch. After one year, lift the tarp and replace the nitrogen in the holes with granulated sugar. Then water the stump again and cover the stump with the tarp and the mulch. The stump will take another few years to decompose but the process will be much faster than natural decomposition.
Rent a stump grinder. A stump grinder is a large power tool with a grinder on its front end. When run back and forth over the stump, it can grind it down to as deep as six inches beneath the surface of the soil. No stump is to big for this job, but a quality machine can be expensive to rent and roots deeper than six inches will remain in the soil until they eventually decompose on their own.
Physically remove the stump with a mattock. A mattock is a hand tool that looks something like a pick axe. The broad end allows you to dig a "moat" around the stump that is roughly two feet away from the stump and three feet deep. Then, the sharp end is used to chop through the bottom of the root ball to remove the tree. This method is quick and cheaper than a stump grinder, but it is hard work, and you may need an axe to help you get through the large tap roots of big trees.