The failure analysis of the soil slope is a very important topic in the field of geomechanics. Being a fully Lagrangian particle method, the material point method (MPM) has distinct advantages in solving the extremely large deformation problem. For both cohesive and noncohesive soil slopes, the large deformation failure problems are analyzed using MPM and the Drucker-Prager constitutive model. For verification of the numerical method, the comparison between MPM and analytical solutions of the dam break problem is presented. Moreover, the numerical results by MPM are compared with the experimental results for the collapse of the aluminum-bar assemblage. Simulations reveal the cohesive soil slope under gravity has a shear band failure mode. Computational results show the reposed angle of non-cohesive soil slope is less than the internal friction angle, and the reason for this phenomenon is presented. The purpose of this study is to give a further understanding of the slope failure in different soil types and provide a computational tool for the failure analysis of soil slopes.