Slow slip and tectonic tremor in subduction zones take place at depths where there is abundant evidence for distributed shear over broad zones (∼10–103 m) composed of rocks with marked differences in mechanical properties. Here we model quasi-dynamic rupture along faults composed of material mixtures characterized by different rate-and-state-dependent frictional properties to determine the parameter regime capable of producing slow slip in an idealized subduction zone setting. Keeping other parameters fixed, the relative proportions of velocity-weakening (VW) and velocity-strengthening (VS) materials control the sliding character (stable, slow, or dynamic) along the fault. The stability boundary between slow and dynamic is accurately described by linear analysis of a double spring-slider system with VW and VS blocks. Our results place bounds on the volume fractions of VW material present in heterogeneous geological assemblages that host slow slip and tremor in subduction zones.