I believe the joke is, "pulling the stick" as in.......removing it.......

;-)

Yes, most aircraft, pulling the stick either deepens the spin, or, (sorta worse) makes it a spiral.
Big difference between a spin and a spiral is that a spin will usually stabilize until you escape it, recover or hit terrain. A spiral may mean you "remove the wings" as you either exceed VNE or G loads, possibly BEFORE you hit terrain.

I believe I get the joke.