Bradford pear trees are very tenacious and can be difficult to remove. Sometimes they just become too big to be left alone.
Reduce the Tree
If you are removing a mature tree, you should first reduce it to smaller parts. When removing the branches, make sure they don't fall onto other plants or property. Trimming branches may leave the tree unbalanced. To avoid this, reduce each branch by a similar amount, working methodically round the tree.
Cut the Trunk
Remove the trunk of the tree as close to ground level as possible. There is always the chance that the tree could re-sprout from a section of the roots. Therefore you should treat the stump with a systemic herbicide. The herbicide typically takes two to three weeks to kill the root system. You can dig some of the roots out, but root systems of Bradford pear trees are so complex that you won’t be able to get them all. Use a stump grinder to remove the stump. The dead roots will eventually decay and cause no further problems.
After two or three months, you should be able to plant a replacement tree in the same spot.