Yes. Your neighbour is entitled to cut overhanging branches where they cross the property boundary and hang over their yard. However, your neighbor is not entitled, without your permission, to enter into your property, whether on the ground or above, and to cut or otherwise damage or plants. If they do, you may sue them in Small Claims Court for any financial loss you have suffered. You do not need a lawyer for this. However, you will have to prove the financial value of the trees that were damaged or lost.
The maximum claim that each property owner can make in small claims court is now $10,000. This is going up to $25,000 on January 1, 2010. If two people jointly own the property that a trespasser damages, both of them can sue.