Here's a generic CV joint image to show what's going on here...
The idea is to put a little tension on the axle - labelled as "Halfshaft" in above image - and this should slightly compress the "Lock Ring". A sharp tap with a suitable soft drift on the shoulder of the "Inner race" while putting tension on the joint should allow the "Halfshaft" to pull out of the "Inner Race".
This is all done with the old boot cut from the joint, or at least slid back along the axle out of the way...
The "Housing" remains in the wheel bearings etc.