It was a constant fight with Minky-fuzz debris on the tables, on the floor, on me, and on anything else in the studio. I no longer have this problem and thought I would share my solution.
I put up a hand held vacuum on the wall so it is always charged and ready to go.
I grab it before I ever start to make a cut in the Minky.
I use the back side of my cutting mat because minky fibers stick in the "self healing" cuts--preventing your mat from self healing.
After every cut, I run the vacuum up the quilt edge, gathering all the fibers from that side, then I swipe it across the mat cleaning up any loose fibers there in the cut, and lastly, I vacuum up the cut edge of the extra fabric trimmed from the quilt. It all takes a few seconds and then I move the quilt down for the next cut.
See, the cutting table looks just like it did before I started.
This extra minute or two while cutting, is much, much faster than having to clean up the whole area: floor, table, and everything else in the room!
Unless a customer does not want their quilt trimmed, I always trim for them. It makes such a nice presentation when they receive their finished quilt. Also quite a few quilts are mailed and it makes a considerably smaller package.