This paper presents a novel hybrid deterministic-stochastic river morphodynamics numerical modeling approach that integrates a two-dimensional (2D) hydrodynamic model (deterministic) with a bed morphodynamic model (deterministic) and a bank erosion model (Markovian stochastic). The model solves the 2D Shallow Water Equations and the standard k-epsilon turbulence model. Bedload transport is estimated using the Meyer-Peter and Muller formula, and bed evolution is solved using the Exner Equation. The Markovian stochastic bank erosion model uses a new method to evaluate bank erosion risk. The approach was applied to a meander bend cutoff event in the Maiqu River on the Tibetan Plateau. Sixteen different bank-material critical shear stress cases were considered, representing highly erodible banks to resistant banks. Ten statistical realizations were performed for each case with different bank-material erodibility to obtain ensemble-averaged results. Flow field and bed evolution in the cutoff channel suggest that the model can successfully simulate bank erosion processes during the cutoff channel evolution, and bank topographic irregularities are reasonably captured. A newly introduced calibration parameter, the ratio of mesh size to the coupling period between the bank erosion model and the hydrodynamic & morphodynamic model, is not as intuitive as the erosion resistance calibration parameters used by the traditional bank erosion model. The proposed approach necessitates estimating the size of a typical slump failure, or 10-30% of the cutbank height, to set the size of the computational mesh.