Observations of the neutron star/Be star binary PSR B1259-63/SS 2883 are mapping out the process of the initial spin-down of neutron stars, which turns spin-powered pulsars into accretion-powered ones. I show that valuable diagnostics of ''propeller'' plasma torques due to the matter around the Be star are provided by observations of the spin-down of this and similar pulsars during periastron passage. Close to the periastron, the instantaneous spin-down rate due to propeller torques can significantly enhance or even dominate that due to the usual electromagnetic torques on the pulsar, although the cumulative effect on the total spin-down during the periastron passage may be rather small. Results from the observations of the periastron passages of PSR B1259-63 in 1990 August and 1994 January are consistent with a disk around SS 2883 which is con; siderably tilted from the orbital plane.