I have purchased a home a few years ago
which has a LARGE swamp maple (75 feet) in the back against the garage. According to the survey 3 feet 3 inches from the garage is the boundary line. The trunk is close to 4 feet in diameter.
With that said, the tree has broken through the wall of the garage and the floor is severely heaved.
We want to have it taken down but our neighbor feels it is their tree. It is not on either of our surveys and my town inspector said I should get another survey
taken. What are my options?

This could get to be a real legal issue. generally, you are allowed to trim/remove any limbs, etc overhanging your property. On the other hand, if your neighbor insists that it is his tree, how about suing him for damages to your property? Sounds like a real hassle. I might be tempted to remove any and all parts of the tree on my property - might kill the tree. May be best to consult legal advice.

Yeah, you should probably get additional professional advice. But I think I would point out to the neighbor that whoever owns the tree is responsible for the damage to your garage, and ask about his insurance coverage.

hopefully this doesnt get nasty. if the neighbor says its his let his insurance company pay for the damage. if he isnt going to pay for it or gives you any grief start by going to the township you live in and see if they have a platt map you can look at which should have your property listed and its boundaries and property markers that way you can dig up property stakes (if any) that are still underground. but do the platt map finding first then if you still dont come up with anything talk to a lawyer or just cut the tree down and let it land on his house :P whichever you prefer (kidding obviously)