We also do a cut box for pool training. Pretty simple to set up, grab a milk crate and thread it with assorted wires, lines, fishing line, steel leaders and anything else you tie to it. Use a weight to keep it on the bottom.
The box will let team members try different cutting devices and let them see what works for them on different materials. Divers should also try one handed versus two handed cutting (what happens when one of your hands or arms is hung up ). I don't just carry one type of device, and personally i carry a set of trauma sheers, a zknife like cutter, a pair of wire cutters, and a small knife. The divers should have them on their harnesses and usual stow locations where they are accessible.
Blackout masks also complement the drill. To keep it realistic, divers should have the hand protection on that they usually dive with to see the loss of dexterity.
As far as the pieces that are cut... you can have divers work on their knots and such have them hand them to their tender. Basic stuff like a bowline, square knot, and a bend.