What can we do if out neighbor’s tree is on our property?

No, you can't simply cut it down. There are three main issues:

1) First and foremost, your survey could be wrong; or, if not wrong, it may contradict a survey the neighbors have. Surveying, believe it or not, is nowhere near as exact as one may think it is; two surveyors often do come up with somewhat different boundaries. So you need to work this out with your neighbor--compare surveys, commission a third survey jointly to resolve discrepancies, negotiate, etc.--because if you don't do that ahead of time, if you cut down their tree and they think the tree was on their land, you'll end up in court after the fact.

2) Even if your survey is accurate, possibly a previous owner granted some sort of easement or right to the neighbors for their tree; that's another thing to explore with them, to see if they claim such a right and have anything to back it up.

3) Even without 1) or 2) above, it's possible that the neighbors have acquired an "equitable easement" in the area the tree is on, if the tree has been there a long time with landlowner permission.

All in all, you can't simply assume that one survey delineates the boundaries exactly and also determines all rights. You should approach the neighbors and first discuss matters with them; you may end up having have a lawyer help you resolve matters, because again, a failure to sort it out ahead of time will likely lead to litigation after the fact.

Finally, consider this: whatever your relations with the neighbors, if you cut down a tree they like, they will be worse than they are now. If the tree only barely encroaches, a better way to do things--and a lawyer can help you--would be draft some agreement with the neighbors whereby they acknowledge that the tree is on your land (so you're not giving up anything) but you agree to let is stand and build your fence around it. That way you preserve your rights while also preserving the relationship (and a tree).