Snap Ring holding axle in place

But that simply holds the assembly from coming through the retainer plate. All you have to do to get the axle out is remove the nuts holding the retainer plate on, bump the axle with the reverse drum as Del described, use a slide hammer if they are really stuck and they will come right out as an assembly. There's no need to remove any snap ring to get the axle assembly out.
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That's all right. But it was stated that the clip is to keep the axle from going further into the rear housing that is not the case. The clip is to keep the axle with the bearing from coming out of the housing. The whole assembly depends on that clip to keep the axle in the rear end housing without that clip the bearing will slide through that outside retainer plate and you will lose your axle wheel whatever.

The axle cannot go in any further to the housing than the bearing will allow it.