Can an axle be removed from this Technic 'brick paradox'?
I reproduced the problem and got the axle out using a sculpting tool (similar to an awl). It's a sharp point made of hard metal. (Soft metal will actually bend, believe me, I tried three tools.)

I inserted the point in the space left by the axle groove and pried the axle out. The point of the tool was against the axle while the body of the tool was pushing against the beam's rim. I made a short video to explain.

After looking at the pieces, I saw that it did however leave some damages to both pieces. On the axle it is barely noticeable, While the rim of of the beam has some little notches.  Because of these small damages, it's not something I would do on a regular basis.  On the other hand, both pieces are totally usable after the 'operation'.