I hate to disagree with
@Adair M on the topic of wiring, but this topic is really about removing wire.
I would rather cut my wire off, one coil at a time.... and only using good bonsai wire cutters, which are snub-nosed and give you great leverage when cutting wire, so the wire doesn't get squeezed and damage your branch, as it would if you used standard wire cutters for electricians.
Un-wiring a branch is unnecessary stress on the branch and if it's starting to bite, you can tear bark off too, when un-wiring.
And if your main goal is to reuse your wire.....stop being so cheap.
Just my humble opinion.
No, I don't unwind to be cheap. I save my old copper to sell to the recycler.
You are not the first person to question me on this. It's a technique I learned from Boon. Who learned it from his teacher, Kamiya. I have the pleasure of knowing many certified Bonsai Masters from Japan, and ALL of them unwind rather than cut off their wire. ESPECIALLY, if it has cut in.
Why?
Embedded wire has only a portion of the wire exposed, right? If you take bonsai wire cutters, the blunt tip ones, you can only cut 1/2 way thru the wire. You can't cut completely thru the wire without first cutting thru some wood to get the jaws of the cutters deep enough to cut entirely thru the wire.
And, I'm sure you've noticed: sometimes if you don't get the cutters exactly perpendicular to the wire, when you cut, the little chunk you're removing will twist as the cut is made. Sometimes if it were embedded the twisting can damage the branch all along where the chunk of wire was.
You may accidentally leave a chunk or two of wire in the tree! Don't laugh, I have found old chunk of wire is several of my clients' trees.
You may accidentally leave chunks of wire on the soil. Again, I've found them when working trees.
Large and really large wire may be too stiff to unwind. Gauge 10 is about the cutoff point. (Pun intended!). Large wire usually doesn't cut in as badly as the small stuff, so you're usually ok. I will unwind any wire I can.
So far I just described the drawbacks of cutting it off.
Unwinding wire is no more damaging that putting it on in the first place. If you have seen any of my wiring tutorials in the Resources Section of this forum, you see I end each end of wire with a little fishhook. The fishhook not only allows me to guide the bud at the tip, it's easy to grab with a pair of bonsai Jin pliers. With one hand spinning the pliers around in my hand, and my other hand steadying the branch one turn back, unspinning allows the wire to lift straight up off the branch. If it's a little (or a lot!) cut in, lifting straight up does the least damage. I unwind all the way back to the anchor point, then find the other end, unwind it back to the anchor, and then pull the wire out. If it's all kinked up and long, you can cut it in half to ease removal.
Start with the small wires first. Those should have been the last wires you put on. Then work progressively back to larger and larger wires.
You will find that you won't accidentally cut thru branches. You dont have to struggle to get wire cutters in awkward places. Your hand holding the pliers never really gets inside the canopy.
Truely, it is both less damaging to the tree, and faster.
Oh, I was a skeptic, too, at first. I told Boon that John Naka had taught me how to cut off wire! Boon said that no one ever told Naka the right way to do it! Lol!!! It did take a bit of practice. But now, I wouldn't consider any other way.