See also origin cut.

Deep cut (of a puzzle)

A puzzle cut where the cutting surface divides two isomorphic groups.

Note there is continued discussion on whether this surface must be planar and/or pass through the puzzle origin.

Source: http://twistypuzzles.com/forum/viewtopic.php?f=1&t=11001

Deep cut puzzle

A puzzle comprised of only deep cuts (see above). The 2x2x2 and Skewb are two examples of deep cut puzzles. The 4x4x4 has all the 2x2x2's deep cuts but also has shallow cuts so it is not considered fully deep cut.