The first thing to do is to establish what kind of tree it is, either by posting a photo for us to ID, or by talking to your neighbour.

Then you need to be clear as to whether these growths are actually seedlings from the tree - my Ash tree produces a lot of 'babies' and they're not only immediately under the tree! These are easily pulled out.

If the shoots are coming from the roots, the easiest thing is to cut or preferably pull them off, or mow them off if they're in your lawn.

A more drastic step would be to dig the roots out amd saw them off at your boundary - but before you did that, you'd have to talk to your neighbour about it, as that might affect the tree.