For the most part, people usually have nice neighbors who take care of their homes. But once in a while, a neighbor and or his pets can be devils from hell. The first thing to do is not confront someone who is irrational. Hopefully, you live in a tract with a Home Owners Association. Odds are pretty good that a bad neighbor is violating some HOA rules. If so, call the HOA and let them handle it. They have the ability to fine a resident who is not following the rules. They can make someone pretty miserable if they don't comply with the rules.
Next, if you don't live in a tract with an HOA, there could be city or county ordinances that apply to what the neighbor is doing. Call your city or county if you live in an unincorporated area and demand that they deal with the problem. You can also call the police or sheriff if you think the neighbor is doing something illegal. No one is allowed to come on your property and destroy any plants, trees etc. They are allowed to trim trees that may be growing over the property line; but only up to the property line.
Hopefully, your HOA or city/county law enforcement can deal with any neighbor that is violating rules or laws. You certainly don't want to create a situation that could turn violent. There are many people addicted to drugs or alcohol that could be very irrational. Do not engage them under any circumstances. At some point, if the problem is not solved, you may need to move. There is nothing worse than dealing with a crazy neighbor. You could try chocolate chip cookies and see if that works.
