Prepare a cleared area where the cherry tree will fall, particularly if it is a large variety. If there is insufficient clearance for a landed tree, then contact a professional tree removal company for consultation.
Cut the tree as close to the ground as possible using an axe or chainsaw. Be aware of which direction the tree is leaning as you do this. Always wear safety goggles when using a chainsaw.
Grind the stump down to its roots with a stump grinder, if immediate and complete removal is desired. You can rent stump grinders at home and garden centers. Remove the sawdust and the nearby area will be ready for growing new plants. Alternatively, you can leave the stump standing.
Drill holes in the stump and apply herbicide treatment containing methyl bromide, if you choose not to grind the stump down. Coat any sprouts that emerge with the chemical. Remove one of the sprouts and replant to grow a new tree in a more ideal spot, if desired.