Disclaimer: although I'm a lawyer, I'm not licensed to practice law in your state, so consider the following to be worth exactly what you paid for it. Talk to a lawyer licensed in your state, because you have rights to protect. If you don't want to get involved with a lawyer, then avail yourself of your local small claims court - everyone has a right to represent themselves in court, and small claims is structured to get relief, quickly, and often without the need of a lawyer.
Here's a general rule of thumb: you can usually do just about whatever you want within the bounds of the law on your own land, unless something you are doing unreasonably interferes with or damages someone else's land.
When you say the trees are encroaching on his property, how so? Are we talking overhanging branches? Are the plants existing on the boundary so that the trunk/stem is sits approximately on the boundary line? Or, are the plants entirely on the neighbor's property?
Most states have specific rules that apply to "boundary trees" - and that usually translates to the trees being treated sort of like a fence. Each party may reasonably maintain their respective side of the boundary - which can include pruning, but not so much so that the tree/plant is harmed or destroyed, and removal if the plant dies or poses a risk to life or property.
Trees and plants rooted in the earth are generally considered part of realty, and harming those trees is a trespass. Try to get your local law enforcement to do a police report or cite the neighbor for whatever is applicable under your state's statutes and/or local ordinances. Call your local state's attorney's office and your local city attorney, too. Trespass citations will likely be handled on the municipal level with the citation issued by the municipal police authority (local police if incorporated or if your jurisdiction is under a cooperative policing agreement, or the county sheriff), and will likely be prosecuted by the municipal court (which would mean the local muny's city attorney or appointed muny prosecutor. Calling the city clerk should get you a name to talk to).
Anyway, depending on your local ordinances and state statutes, this could be called a number of things: criminal/misdemeanor trespass, vandalism, destruction of property, etc., come to mind.
The bottom line? Raise hell with the authorities until they do something. The law tends to frown on self help, so don't start retaliating or you'll get cited and/or sued as well.
Oh, and, like I mentioned earlier. Go talk to a local lawyer with a background in real property and boundary disputes. Get that attorney to get a lawsuit on file.
Were it me, I'd be filing for a temporary restraining order (most immediate type of relief a court can grant, and has force of law if granted to stop a behavior for a limited period of time until a court can better analyze the situation. Hard to obtain because these are usually done ex-parte, and typical judges are wary of granting orders without having all parties concerned present), a preliminary injunction (like a T.R.O., but will be granted after the other party has been served with notice of a court hearing, and a hearing on the record to determine whether to grant the injunction. The injunction, if granted, makes a party do or not do something until the larger underlying question in the lawsuit is determined), and a permanent injunction, which is a permanent order of the court that a party do or not do something, which is to be entered if a plaintiff wins their case on the merits. Violate an injunction or TRO and get fined and/or go to jail along with paying whatever damages are found to be caused. In addition to all of the above, if a tree dies, I'd be suing for the value of the damage. If the trees are damaged, stunted, etc., that has a value too, and the neighbor will owe you that amount.
Trees are expensive, and the wrongful deforestation statutes make them even more valuable. My states don't authorize recovery of attorney's fees in a wrongful deforestation action, but yours might.
Go and raise hell with the local authorities, and talk to a lawyer.
