The first step is to look at the one you did manage to dismantle to see if you missed something - unless it is rusted it shouldn't be that hard to take apart. I can't tell much from the picture except that one has a retaining nut, and the other doesn't. I take it the one without the nut is the one you are trying to dismantle, and you've already removed the nut.
It looks as if you begin by removing the V-belt pulley. If it was held by a nut, it must be capable of sliding off, or they wouldn't have needed the nut. Can you fit a split plate under the pulley, so it bears close to the shaft, not near the outside of the pulley, and press it off? You may need a special split ring, to make it bear in the right place on the underside of the pulley. This would be a small lathe job. Don't let the split ring bear against the outside of the pulley, you'll just crush it.
Once you have ensured there is no secret retaining device we don't know about, it is just a matter of supporting the underside of the hub of the pulley, and putting ten or fifteen tons on the shaft with a good press that pushes square to the split ring. It is good practice to put a piece of aluminium between the press platten and the end of the shaft, so the shaft doesn't deform. When the shaft moves the length of the threaded part, you'll need to use a piece of axle-sized steel bar with square ends, in between the platten and the end of the axle so you can continue to press the axle downward. Aside from having to make the split ring if you don't happen to have a suitable one, it is routine.
