The graveyard spiral is a classical "unstable system". The long answer to this topic is found in the study of aircraft stability, flight dynamics, handling qualities, and more generally system dynamics. You won't see these topics in flight school unfortunately- they are engineering subjects for the most part.

But in a basic way, pitch, roll and yaw axes are defined in relation to the airplane body while flight path and gravity are defined in relation to the earth. So when you roll past a certain point the vertical component of lift goes to the horizontal. The airplane was trimmed for level flight, which means it was stable there. So, it starts descending in an attempt to get back the vertical lift lost, which can only be had by an increase in airspeed per the lift equation. It trades potential energy in the form of altitude for speed (kinetic energy) to get more lift. It descends a little at first.

A mild bank, perhaps a wind gust caused the original loss of lift. The airplane could actually could find a new equilibrium by speeding up in level descending flight, we do this all the time to descend. But in this case the outside wing begins to develop slightly more lift than the inside wing, something it is supposed to do. Lift on the outside wing goes up with speed, increasing the bank. As the airplane has a tendency to roll towards its slower wing it loses even more lift to vertical and the airplane must now speed up even more.

Now going back to the original issue, which was a loss of lift. We are losing even more now, so the airplane has to seek a faster speed to get that equilibrium it needs. It is an unstable system that continues until all the available energy is used up and the altitude runs out. The end of that of course is a crash, and I suspect investigators using radar tracks and flight data recorders have linked a few to spiral dives.

As long as the roll has not exceed 90 degrees the airplane could possibly be recovered from the turn by merely pulling up on the yoke. It will exceed its structural limits at about n = 4, however. The right response is to therefore to remove bank first to get the real energy waster out of the equation, then recover by any of a number of actions which may or may not include pulling back on the yoke. You may need to apply back elevator, possibly no elevator if it was trimmed for level flight, or even forward pressure depending on how it responds. You are flying at speeds you did not expect most likely, perhaps quite surprised as well. You need to go a little slow on the recovery until speed is under control.

I do steep spirals at 70-110 degree angles all day in my part-time skydiving job. Speed is about 150 mph. The graveyard spiral is tame if you manage things properly. If airspeed goes crazy you always roll out first then adjust pitch. As explained that could be either way, pitch up or pitch down. I actually do them kicking full rudder in a slip, which gives a knife edge maneuver. I put some pictures up a few months ago of this from my own airplane in the Your Photos section (see Knife Edge).

Here's one of my favorite non-engineering links on the subject.

Denker on Steep Spirals