Millisecond pulsars are old neutron stars that have been spun up to high rotational frequencies via accretion of mass from a binary companion star. An important issue for understanding the physics of the early spin evolution of millisecond pulsars is the impact of the expanding magnetosphere during the terminal stages of the mass-transfer process. Here, I report binary stellar evolution calculations that show that the braking torque acting on a neutron star, when the companion star decouples from its Roche lobe, is able to dissipate >50% of the rotational energy of the pulsar. This effect may explain the apparent difference in observed spin distributions between x-ray and radio millisecond pulsars and help account for the noticeable age discrepancy with their young white dwarf companions.