Hello Martin,
The axle may be hard to saw but I would not have thought it would be made out of stainless steel.
This is a comparitively expensive engineering material and holds no real merits for a nearly totaly enclosed axle. A magnet might prove the point.
But anyway, that does not answer the question posed:-
I am not familiar with your setup as I have used wheel chair motors similar to the ones supplied by Richard of Toylander, but I would have thought that provided the cutting is done in short runs and the temperature of the diff. oil is felt to make sure there is no sign of overheating, then this should result in an amputated lump of whatever metal.
I would make sure that the hacksaw blade is new and tightened up well and try an 18tooth blade as a starter, be carefull as the blade bites deep, as cut might grab the blade and these motors have a fair amount of torque which could do you some serious damage under a worse case scenario.
No loose clothing and some one adjacent to switch off while you are doing it please, just in case.
Regards,
Brian