When a propeller blade goes supersonic, it produces a supersonic compression zone (shockwave) just in front of it. That shockwave then travels over the propeller airfoil (from leading edge to trailing edge at any point along the chord of the propeller) when the propeller is moving (rotationally) faster than the shockwave. Additionally, if the aircraft continues to accelerate to the point that the wings go supersonic, the propeller is subjected to a second shockwave - that of the air rushing at it from IN
FRONT of the aircraft. This "longitidunal-aspect" shockwave is separate from the "rotational-aspect" shockwave that is created by the rotation of the propeller blade through the plane of the propeller disk.
A designer can overcome the drag from the rotational-aspect shockwave simply by increasing the propeller RPM at the moment the leading edge goes supersonic. What is extremely hard to overcome is the longitidunal aspect shockwave that is hitting the "top" surface of the propeller airfoil (i.e., that air which is coming directly at the front of the engine, 90-degrees to the plane of the propeller blade rotation.) When THAT shockwave encounters the rotational-aspect shockwave somewhere along the "top" of the propeller airfoil, the resultant interaction creates some very tricky, if possibly unmanageable, forces on the air the propeller is trying to push aft.
This interaction of two shockwaves colliding with each other along the "top" of the propeller airfoil produces many different effects, one of them being a sudden "overpressure zone". That zone spreads from it's initial start point along the airfoil chord all the way to the trailing edge of the propeller, where it meets the high-pressure zone from the "bottom" side of the airfoil. Extreme turbulence at this juncture then creates high-low-high pressure zones at the aft edge of the propeller, which then propogate somewhat forward onto the "top" of the propeller airfoil.
These high-low-high pressure zones then set up harmonic vibrations along the propeller airfoil chord that can be so great as to totally destroy the propeller in seconds. This is not exactly the same as what was happening when all the Lockheed Electras were crashing during the late '50's and early '60's, but it is close. The propellers on those aircraft actually "went supersonic" in two separate axis (longitudinal to the aircraft fuselage, and rotational to the plane of the propeller disk). The props / engines / engine mounts / wings were not designed to handle the ensuing harmonic vibrations, so things flew apart.
"There may be old pilots, and there may be bold pilots, but there are darn few green cows"