Kill the tree and be in for some trouble. Trees cause more disputes between neighbours than anything else. Spot spray suckers and you'll be waiting a life time if you wait till the suckers stop. If the soil above the roots is disturbed, that is often all it takes to send up a sucker. A fork or spade can hit the root and the natural response of many trees is to send up a sucker.
For future reference:
Never plant trees on a boundary unless you have had good advice and clever tree selection for the area.
Get the right tree.
Get the right advice.
How do you get the right advice? Well right here at Homeone is a start, but also from your local certified arborist.
http://www.treesaregood.org/findtreeser ... rvice.aspx
A Horticulturist is good, an Arboriculturist goes on from there and studies a further 4-5 years just on trees after the 3-4 years they did to be a Hort That should give you an idea of the knowledge they have