We demonstrate that ``hot'' MHD outflows from neutron-rich black hole debris disks can significantly alleviate the baryon-loading problem in gamma-ray burst sources. We argue that the neutron-to-proton ratio in disk-fed outflows might be as high as ~30 and show, with the help of an exact semianalytic relativistic-MHD solution, that the neutrons can decouple at a Lorentz factor γd~15 even as the protons continue to accelerate to γ∞~200 and end up acquiring ~30% of the injected energy. We clarify the crucial role that the magnetic field plays in this process and prove that purely hydrodynamic outflows must have γd>~few×102. The motion of the decoupled neutrons is not collinear with that of the decoupled protons, so, in contrast to previous suggestions based on purely hydrodynamic models, the two particle groups most likely do not collide after decoupling. The decoupled neutron flow might nevertheless contribute to the observed afterglow emission.