If your machine has a front loading vertical bobbin, a surgical seam ripper does well. You lift the hoop or fabric just enough and swipe the tangle with the seam ripper. Then you can move hoop or fabric and clean up all the threads.
http://www.amazon.com/Live-Guides-Ka.../dp/B003L80N4Q
It's more used with sergers, but it does wonders on tangles. I have a Pfaff 2170