A theory is introduced for spin relaxation and spin diffusion of hopping carriers in a disordered system. For disorder described by a distribution of waiting times between hops (e.g., from multiple traps, site-energy disorder, and/or positional disorder) the dominant spin relaxation mechanisms in organic semiconductors (hyperfine, hopping-induced spin-orbit, and intrasite spin relaxation) each produce different characteristic spin relaxation and spin diffusion dependences on temperature. The resulting unique experimental signatures predicted by the theory for each mechanism in organic semiconductors provide a prescription for determining the dominant spin relaxation mechanism.