Get a very sharp spade, and dig along the border to sever the roots. If you can, dig a trench and put a physical border below the ground between your neighbour's plot and yours - something like tiles or paving slabs laid vertically. If you have an allotment you can sometimes get hold of galvanised sheeting, or maybe heavy duty plastic sheeting (sorry, I'm thinking on my feet as it were). If you can stop the shoots migrating from his plot to yours, you should be able to clear yours by digging and/or pulling out new shoots as soon as you see them.