To give those of you wondering about the process just a little idea of how it goes, here's what I've got.
First, a couple of snips, and pull. Here's what you get.
Then you can remove individual pieces with the same steps.
This sweater was a little different because once I actually unraveled each piece, I had to separate the yarn into two pieces. Two strands had been plied together (think two-ply toilet paper). So, I unraveled each section of the sweater, un-plied (is that a word?) the two strands, and then wound the individual strands into balls.
I ended up with 5 balls of lovely yarn. In the picture you can see the start of a single crochet scarf. I wanted to see what it would look like once it was worked up. I was also experimenting with hook size.
Guess I better add the scarf to the UFO list in the sidebar.