If the neighbor is a Community neighbor, simply click on the 'Neighbors' button at the top of your game screen, open the 'Community Neighbors tab', tick the box next to the name of the neighbor you wish to remove, and click 'Remove'.
If the player is a Facebook neighbor, then you can remove the player if he/she has been inactive for 2 weeks by hovering your mouse over their icon on the neighbor's bar. After doing so, a little red remove button will appear on the lower left of their icon. Click that to remove that neighbor.
Or you can try to remove them from your FB friends list. If you ever have a problem removing neighbors by yourself, please feel free to contact us with the friend's SNSID/FB profile name. We'll be more than happy to help you with that.