I wouldn't cut anything off of or at the posts. Yes, cut the sections free from each other (if desired, see last paragraph), but leave the horizontals or at least 6" inches of them on the posts (the more the better).
The reason for this is that you can likely just pull everything out of the ground by the fence itself. Using a double 2x4 on a board a couple of feet from the fence can typically make you Superman & pop that post & it's concrete right out. You'd increase your yard board's thickness or height as the post comes up to maintain your optimal leverage.
Otherwise, I prefer a see-saw type of setup where I just use my body weight. You'd start with a cinder block or stack of wood a foot or 2 away from the post which is about the same height as a horizontal & just pull down & push down the double 2x4 to pop out the whole fence assembly. You'd increase the height of your fulcrum as or if needed until the post is out & free.
You don't even need to cut anything & can just work your way up & down the entire length of the fence incrementally...if you could actually use the fence somewhere else.