Privacy trees screen your yard from the neighbours, and their backyards from you. When someone wants to prune or remove privacy trees, your range of actions depend on who owns the tree.
Whether your neighbour has the right to cut down privacy trees depends on where the trees are. If they're your neighbour's trees, she can cut the trees if she wishes. If the trees are growing in your yard, however, but some branches fall into hers, she can trim the privacy tree back to the property line but no further. If she trims trees in your yard, she's breaking the law.
Some trees fall on the property line between houses. In this case, you maintain the side of the tree on your yard, and your neighbour takes care of his. This means he can trim his side of the tree as much as he wants. You would both need to agree on removing the tree, in that case.
If you have good reason to want the tree, try talking to your neighbour. Politely ask him not to trim the tree, then see whether he'll honour your request. Both of you have to follow the law, first and foremost.