Answer: Once you've cut the roots off they will probably callous over and stop sending out new shoots. To make sure they don't invade again, you may want to place a barrier along the property line. If the tree is shallow rooted, you can pour a concrete footing along your side of the property line to stop the roots. Dig a trench 12-18" deep and 4-6" wide and fill it with concrete.
Good luck with your landscape.
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