The safe and sane way is to press them off. The old-timer way was to break off the outer shell with a big hammer, remove the balls, heat one spot on the inner race until it is red hot, smack it with the big hammer and the bearing will fall off. Obviously this may mess up the temper of the axle if not done quickly before heat transfers to the axle from the bearing race. Having the axle break at the bearing while driving down the highway will ruin your day (not to mention your car).
There's not much room to get in there with a cutoff wheel, but if you notch it as much as possible you can drive a cold chisel into the notch and break the race.
And then you have to install the new bearing. Once again, a press is the best way. Back to the old-timers, they used a length of pipe to drive them on with the big hammer. To me that is a good way to mess up the bearing, and at a minimum destroy the seal. Too much work involved in changing an axle bearing to have to do it again in a few weeks.
So, either buy yourself a press and bearing separator, or take it to a machinist or mechanic who has the tools.