•The NMM is used to conduct stability analysis of soil-rock-mixture (SRM) slopes.•An improved shear strength reduction technique is implemented into the NMM.•Influence of rock blocks on the stability of SRM slopes can be captured by the NMM.•Failure pattern of SRM slopes is different from that of a homogeneous slope.•The advantages of the NMM in discretization and accuracy are demonstrated. Recently, fruitful results of geotechnical problems solved by the numerical manifold method (NMM) have been gained. In the present work, the shear strength reduction technique (SSRT) together with the ϕ–υ inequality is implemented into the NMM to carry out stability analysis of soil-rock-mixture (SRM) slopes. Several examples are used to validate the correctness and effectiveness of the developed numerical model. The results from these examples indicate that the proposed model can predict the factor of safety (FOS) of slopes with high accuracy, and capture the failure patterns of slopes. In addition, the influence of rock blocks on the stability of SRM slopes can be captured.