Step 1: Cutting Through the Box Springs
I measured the cushions on a regular couch to find out where to cut the two ends of the box springs. I wanted an L-shaped sitting area formed by two sections but you can create any configuration you like. Look at the bottom of the box springs and see where the wood cross pieces fall. It's important to cut it so that one is left to form the new back line. This maintains the box integrity. In my case this made the bottom section slightly narrower than the mattress section on top of it. But in the end the overhang made it more comfortable to sit down and stand back up.
Cut through outer covering and padding
Use a regular pair of scissors to cut through the covering right down the center. This was my exploratory cut. See how yours is constructed before you open it up too much. Peel the covering back. You will now be able to see into the box springs. Measure the two ends and mark the cut on the springs themselves with a Sharpie pen (I used blue so I could see it better). Remember to make this mark longer so that you can bend the cut end over. You don't want the metal rod poking straight out through the fabric.
Using a Dremel tool with a Fiberglas reinforced cutting wheel cut down the line of springs (see photo). Make sure to wear eye and ear protection and gloves because the sparks smart. Hold the tool steady because any jerky movement will break the wheel. Depending on your mattress you may want to cut the springs longer (the height of the box springs) and then use pliers to fold the wire down forming the back wall of the new section. I tied the folded down wire with cotton rope to give it more support.
If it is possible cut the wood leaving a supporting crosspiece to form the back line of the new edge (see photo). If this isn't possible nail a crosspiece along the back edge.
Close up ends by pulling covering and padding back into place. Wrap it around to the bottom of the wooden crosspiece. Staple in place and trim excess. Then pull the bottom thin fabric (looks like interfacing) and staple it back on and trim excess.
Repeat on the other end of the box springs to form the two lower platforms.