In rockcrawling, you have to deal with big 1.5" alloy shafts. When they snap, the shaft can blow right out of the axle tube itself. Damn scary!
I have found that a great way to remove the end thats still in the tube, along with any fragmentation, it with an magnet. You can order rare earth magnets online. Just epoxy one to the end of a wooden dowel or a non ferris metal pole, and bingo!
Then you can grab the shaft and pull it right out.
*Only in automotive forums can you say that and not have it misconstrued.*