If you wanted to cut only part of an object, you could move it to the edge of the mat, and the portion that is outside of the "cutting area" (the 1/4" margin on the mat) isn't cut.
However, if you move the right-hand side of the object off the mat, you lose the resize handle in the bottom-right corner of the object.
If you try to move the left-hand side of the object off the mat, good luck if your SCAL application is maximised!

And if you have managed to get the left-hand side of the object off the mat, you can no longer move it -- at least not that I can work out.
Having these handles in fixed positions on the edge of the object is very restrictive -- the design for these operations needs to be improved.