Dealing with springs
Recycling mattresses best means that you are left with spring bases. These bases become problematic, because they are not particularly dense, and the spring steel can cause problems for scrap metal shredders.
Olaf Industries has come up with a baling solution for the mattresses, and Mission Australia's Soft Landing is distributing them in Australia. Have a look at the video below to see what it can do.
In case you missed the box spring dismantling, here's another video of one of those. It doesn't seem to do quite the same job as the Goodwill Industries machine.
Then there is the option of shredding the springs. There is a pretty cool video of a shredder chomping up all sorts of things. You kind of half expect the thing to chomp up the operators - their safety guarding is not the best.
Robotic mattress dismantling
And finally, the news that got me started on all of this, the Baxter Robot. It's a robot, that's not so exciting. The exciting bit is that it sells for $22,000 (USD). I can imagine a robot cutting apart mattresses using rotary cutters in a way that may be too dangerous done by people.
Unfortunately they are not for sale outside the US.
Maybe it doesn't need to be a robot. Maybe a rotary cutter running back and forth on a rail, with the mattress turning so that each side is cut. I wonder if that could be designed up by a clever mechatronics engineer.