You have what sounds like a single bearing alternator, and the long threaded stud which passes through the centre of the alternator shaft has the effect of pulling the rotating part of the alternator onto a tapered shaft which in turn usually forms part of the engines crankshaft, but on bigger engines is usually an adaptor shaft which bolts to the flywheel.
You need to loosen the nut on the end of the alternator shaft as you have already done so, and from here on in it can get a little tricky, as you need to break the taper between the engine and the alternator.
The easiest and least likely method to cause damage is to remove the bolts holding the alternator to the bell housing of the engine, then carefully open the gap between the engine and alternator at the bell housing joint face with fox wedges or similar. Once you have some load on the alternator shaft, carfully hit the end of the alternator shaft (where you removed the long threaded stud from) with a brass drift or soft mallet. This should be sufficient to break the taper.