You'll most likely want to remove the wrapped wires before processing (there's no sense in mixing the silver-plated copper in with the gold-plated stuff).
Oh, it looks like a slow and painful process - don't worry - it is!
But, there's a special tool for it, looks like a tube with a little hook on the end of it which gets the unwrapping started. Then, it is just a couple twists to loosen it enough to pull off. They also make a quickie hand tool (looks like a little pistol) and even an attachment for a drill/electric screwdriver (talk about getting those wires off FAST!
Hardly worth the investment if you are doing only one board, but with as many wires as you have, and over time you will likely get more (if you stick with gathering gold, you will.... - so, you will need one.
I don't have a link for any of them, but a search for 'wire-wrap tool' should bring up several options. I used to have one in my tool box when I did a lot of wire-wrapping many years ago (when we built prototype boards, but also used a LOT in the telecom industry - at least up until 1995, when I got out of it).
If someone knows of a good place to get a single tool (haven't checked, maybe Radio Shack?), I'd be interested. I've got some backplanes out of a 'new' Cisco router that has a ton of wirewrap on it that I need to clean up one of these days (when I get so totally bored that I'll dig into it!
