Can I cut branches from a tree on someone else's property which hangs over my property?

The short answer is yes (see Macero v. Busconi (12 Mass L. Rep 521 (2000)) and Michalson v. Nutting (275 Mass 233-34 (1931)). It is strongly recommended that you work with your neighbor in order to resolve this issue. If you cannot resolve the matter, consult with your attorney to determine your full rights and responsibilities in the matter before taking any action.