I'm not an expert so this is not guaranteed!
I would trim off the small branches from the upper side of the main trunk. These can be dragged away quite easily to be cut up for logs or just burnt.
You may be able to lift the trunk at the 'top' end a little. If so, put a small log under the trunk to keep it off the ground and then cut off the raised end. Again, it can be cut into logs or dragged away and burnt.
You can repeat this, keeping a small log under the main trunk to lift it slightly and cutting through it just over the log where the upper surface is in tension. That way it doesn't jam the saw before the trunk is cut through.
If you have a length of chain or a tow rope, you may be able to pull the remains of the trunk - at the smaller free end - using your tractor and the chain/rope. If so, you can try to break the trunk from its root end.
Obviously, be careful. Also, you can damage the grass and finish up with it looking like the left overs after the Battle of the Somme!
By the way, I got my local tractor workshop to make me a 5m length of chain with a small hook on each end. I use this to loop around bit of tree and hooking the chain onto itself. The other end goes round the tow bar on my 4X4 or the hitch on the tractor. Then I tow the timber to a central point where I can cut it into logs and leave the small bits to pile into a bonfire for disposal.
Good luck
NN