Combining shapes when drawings, but separating for CNC machining . . .

 From:  Alligator
5825.1 
I'd like to design a box, focusing on each side separately. However, I'd like to design it all in MoI so I know the pieces fit together correctly. Then I need to machine each piece with my CNC machine, and it will need to process one side at a time. What is the best way to break the design apart so I can machine it? Can I cut and paste each side into a new file? Or is there an easier way?