I find the original reference seems to be here. I still do not understand the mechanism. It is necessarily occur in neutron binaries? Anyone can introduce it in detail? This paper is old.
The magnetic field of the rapidly rotating neutron star interacts with the material coming from the other star in the binary. This results in a transfer of angular momentum, spinning the neutron star down but accelerating the material out of the system. The effect is somewhat like a garden sprinkler seen from above, with material flung out ("propelled") of the system.
I think there needs to be a quite delicate balance between the binary period (or separation) in the system and the strength of the magnetic field and rotation rate of the neutron star to form the propeller effect. It seems to happen most in the early stages of the X-ray binary when the neutron star is rotating rapidly. After the neutron star spins down by the torques exerted on it, the material from the secondary star in the binary forms either an accretion disk or is directly accreted onto the neutron star down the magnetic field lines.
The effect has also been seen, possibly only the once, in Cataclysmic Variable (CV) systems, which consist of a low-mass star (typically a K or M dwarf) and a magnetized white dwarf. The "poster child" for this type of propeller system in CVs is AE Aquarii A magnetic propeller in the cataclysmic variable AE Aquarii; Wynn et al 1997
The propeller theory seems to be alive and well as there over 800 citations to the original 1975 paper. A recent highly cited review discussing propellers and accreting neutron stars seems to be Alipar 2001