When it comes to tree removal, stump removal is almost never included in the price. Unless you pay extra for this service, you will usually be left with a stump. You can rent hydraulic tree stump grinders, but they are usually only designed to handle small stumps. Stump grinding is a common way to remove the visible part of a stump from the landscape, but it does not remove the root system.
If the stump is more than half a foot tall, the tree removal company will cut it almost to ground level before grinding the rest. Removing stumps from trees with a chainsaw is possible if you have the knowledge, but it can be dangerous. Stumps left in place can make a yard look neglected and unkempt, especially if they grow shoots or harbor weeds and fungi. Milling stumps could cost a little more, as the whole root ball is usually exposed, which means more work to clean.
It will be less expensive to include stump polishing in your original quote than getting a separate quote at a later date. Depending on the tree service company, stump milling can be done on the same day of extraction or scheduled on a different day, as it requires different equipment than tree removal. Usually, stump removal involves the use of heavy machinery to remove the entire stump and part of the root system, but other methods may work under the right circumstances.