I agree with Sparky... a 3PH winch is a great way to deal with trees lkie what you have. I have one on my Kubota and it allows you to work a safe distance away.
The up-rooted tree will need to be severed from the root ball. As already noted that root system is going to want to go back where it was in the ground very quickly once the tree stem is cut. I would notch the bottom side of the trunk with a 90 degree notch. That is make two 45 degree cuts to remove a 90 degree wedge.
The best way to cut the rest of the trunk would be a bore cut through the stem at the same level as the center of the wedge leaving a couple of inches of hindge wood. Continue this cut toward the top of the stem until you have two or three inches of wood holding at the top.
Then finish the cut from the top down. As soon as you make this cut the root system will quickly head for the ground and the tree should rotate on the stump and be pulled backwards by the hindge wood possibily pulling it out of the tree it is lodged in. If it still stays hung you and connected to the stum you will have to carefully cut it free, sometimes cutting one side of the hindge will alow the tree to roll out of the one it is caught in.
The 3PH winch come in handy for pulling the hung tree out. Every situation is different, sometimes a sidewards pull works sometimes pulling it backwards works. Just stay out from under any hung tree, you never know when it could come down on it's own.
Becareful out there.
Randy