In this paper, shear rate-dependent rheological properties of mine tailings taken from abandoned mine deposits prone to mass movements are examined using a commercial ball-measuring rheological system. The yield stresses (i.e., dynamic and static yield stresses) and viscosity of sand-rich materials are examined by the shear rate-controlled flow curve and time-dependent stress growth methods. Before yielding, the shear stress reaches a peak value (i.e., yield stress) observed for all flow curves. In the steady-state condition, the materials have a minimum shear stress (i.e., dynamic yield stress). The static yield stress can be determined under a constant applied shear rate with different initial values ranging from 10−4 to 10−1 s−1. As a result, the Bingham yield stress and viscosity can be used as a first approximation for estimating the debris flow mobility of post-failure materials. However, the Bingham yield stress is competitive with the static yield stress measured from stress growth methods. Upon comparison of the dynamic and static yield stresses, the static yield stress is approximately 35–45 times greater than the dynamic yield stress, and may be strongly related to microstructural changes (i.e., thixotropy). In this context, special attention must be paid to the determination of yield stresses in debris flow mitigation programs.