So my neighbour is building a new house and decided that he wanted to build a new fence in between our house and theirs. There is already a fence in between our houses so he has to tear it down. The fence is on his property but because he decided he wanted a new fence to bring up the value of the house he is building he wanted us to pay for half of the new fence. We politely let him know we @eren't interested because we have no problems of the old fence. Currently he is tearing down the old fence that is on his property clearly and dumping all the fencing debris onto our property and refuses to take it to the dump. What should I do?

Call the police and report him for dumping. I would not throw it on his property because he could call the cops on you. Sounds like an unreasonable guy so no further conversations are needed

... Currently he is tearing down the old fence that is on his property clearly and dumping all the fencing debris onto our property and refuses to take it to the dump. What should I do?

The only explanation that makes sense, other than his being the kind of person who does everything he figures he can get away with, is that he is under the mistaken belief that the fence is on your property, and that you somehow gave him permission to tear it down.

At the same time you do what ballengerb1 suggested, you might send him a letter, for future reference if you litigate, clearly stating the true situation. Use certified mail (or the equivalent in Canada).