Another method to remove the axle is to use a small gage (1/8"/3mm) steel cable and a sledge hammer (as a dead weight).
Form a loop using an eyelet/eyenut and thread the opposite cable end around the backside of the seat/splined/small end of the cv axle, transmission side, and through the loop; pull to tighten it so it can't slip off. With the other cable end leading out past the wheel well, secure to the sledge hammer/dead weight. A swing or two with increased intensity and off she comes! Beats being underneath the car trying to pry against the transmission, etc. while on jack stands/blocks with limited space.
Upon installation of your new axle, dab a bit of grease on the C clip shaft end to assist in seating the c-clip, and perhaps if the need arises again, to aid in removal of the axle down the road.