The material point method (MPM) has been widely used in the simulation of large deformation problems involving hydromechanical coupling recently. Here, an explicit stabilized formulation of hydromechanically coupled two-phase MPM with zero air pressure for both saturated and unsaturated conditions is presented, and to avoid numerical instability when low-order MPM is applied to hydromechanically coupled problems, techniques including low-order shape functions based on the Hu-Washizu multi-field variational principle, the B-bar matrix, and the reduced integration are implemented in the algorithm of MPM. The accuracy of the formulation is verified through numerical examples involving the consolidation problem and Liakopoulos drainage test, and then, two cases, the unsaturated slope failure under rainfall infiltration as well as the Yanyuan landslide, are performed. The simulation results further demonstrate the capability of the present formulation to capture the hydromechanical behavior as well as the failure and post-failure stages when modelling hydromechanical large deformation problems.