The first question is: does the turnbuckle have two cages and a central, double threaded stud? Or a central cage and a stud at either end?

In the first case, once the turnbuckle is apart, you should be able to slide the cage up the rod and expose the head of the rod. This is where you would chop the rod to take off the cage. In the second case, if the rod dissapears into a stud, there is threaded insert of some sort that captures the rod head. Sometimes these are secured by pins, sometimes they are "dinged" - which renders them more or less permenantly attached.

All that said, if you have to cut the rod to change a turnbuckle, it is obviously a shop job - not so much for the cutting but for the re-heading. The fact that a turnbuckle is broken, however, is cause for concern that the rod gang might be ready for a serious overhaul, inspection, etc. Lots of the central-stud variety turnbuckles had stainless studs and stainless cages which made them very suspect to galling and failure down the road.