There is a big oak that died from the drought that my brother in law wanted to cut. It looks to be more than 4 feet across at the bottom. After looking at it, I decided that it is best to just let it stand where it is till it falls naturally. I don't have a saw large enough to cut thru even cutting from all sides. Nature will take it down eventually. The tree you have will rot even in the air. If it isn't in the way, just leave it be. You might remove some dirt from the root ball and fill in the root ball hole a bit if you have the equipment to do that. Even de-limbing it is dangerous as it can come down on you unexpectedly. I have cut up 3 large oaks this year due to storm damage. I de-limbed the sides leaving the stuff on bottom holding up the tree, then just use my LS P7010 to pull the whole tree over so it is laying flat on the ground. Without having the large tractor, I would have just left them in the air.
Whatever you do, don't do any cutting while standing on the tree, if will eventually overcome gravity and flip back upright. If you are standing on it when this happens, most likely you will be damaged or killed. I had an uncle killed doing exactly that when the tree sprang up and tossed him off.