Landslide-induced barrier dams pose a threat to the safety of humans, livestock and nearby infrastructures. The efficient assessment of landslide blocking river is crucial for disaster prevention and mitigation solutions. This study proposes a novel stochastic assessment framework to evaluate the landslide blocking river through the prediction of their deposition depths and considering the heterogeneity of shear strength parameters on the potential sliding surface. The depth-integrated continuum method (DICM) is used to simulate the landslide runout process. Using an enhanced Karhunen-Loève expansion (KLE) method, the spatial variations in soil's shear strength parameters are modeled by random fields to incorporate the effects of soil's spatial heterogeneity on the landslide deposition pattern. Subsequently, the multi-response surrogate model is constructed to relate the random field variables to the deposition depths based on extreme gradient boosting (XGBoost). To improve the performance of the surrogate model, principal component analysis (PCA) and sliced inverse regression (SIR) methods are employed for the dimension reduction of output and input variables, respectively. Furthermore, the algorithm for river blockage identification is developed to search for the deposition ridges. To demonstrate the capability of the stochastic assessment framework, an example of the first Baige landslide in Tibet, China is simulated, and the affected region and deposition depths of the landslide are predicted to calculate the probability of river damming. The presented methodology provides a practical means for improving the landslide blocking river prediction and new insights for early warning and risk mitigation.