To investigate the stability of a soil-rock-mixture (SRM) slope subjected to sequential excavation, two modifications are made to the numerical manifold method (NMM). One modification is the implementation of sequential excavation algorithms including an algorithm to find the excavated manifold elements and an algorithm named as “manifold element birth and death” to remove the excavated manifold elements in the excavation simulation. The other modification is the implementation of an improved shear strength reduction technique to evaluate the stability of a slope, as well as to obtain the factor of safety (FOS). In this technique, apart from the shear strength parameters, the Poisson's ratio υ is also adjusted for the purpose of eliminating the spurious plastic deformation that may happen in the deep areas of the slope. Two criterions including the NC criterion (Non-convergence criterion) and DPZ criterion (The criterion based on the distribution of plastic zones) are used to define the critical equilibrium state of the slope. With the improved NMM, three numerical examples including a homogeneous slope under one step of excavation, a slope under three steps of excavation and a SRM slope under two steps of excavation are solved. The simulation results show that: (1) the improved NMM is able to accurately simulate the excavation process of slopes, and predict the FOSs of slopes; (2) the FOSs based on the NC criterion are usually greater than or equal to those based on the DPZ criterion; (3) it is very difficult to form a slipping surface passing from the toe of the SRM slope to the top of the SRM slope; (4) rock blocks have some positive effects on the stability of a SRM slope. •The NMM is used to simulate sequential excavation of a soil-rock-mixture (SRM) slope.•The sequential excavation algorithms are proposed to simulate the process of sequential excavation.•An improved shear strength reduction technique is adopted and implemented into the NMM.•Results obtained from NC criterion and DPZ criterion are compared.•The advantages of the NMM in discretization and accuracy are demonstrated.