When a tree is cut down the stump is left behind which will usually die within a few days or weeks depending on the tree. Some stumps will produce sprouts which if cut will result in the final death of the root system.
The stump can be removed to varying degrees and depths depending on the requirement and or future plans for the land. Depending on the situation stumps can be removed by winch or by stump grinding machines. The stump, cuttings, sawdust and land can be removed or left as agreed so as to leave the site as you want it.