Land use/land cover (LULC) and climate change are major driving forces that impact ecosystem services and affect human well-being directly and indirectly. Under the future interaction between LULC and climate change, the impact of different land management and climate change scenarios on water-related services is uncertain. Based on this, the CLUMondo model, which focuses on land use intensity, was used to simulate the land system under different land management scenarios in the future. By coupling the downscaled climate scenario data, this study used the InVEST and RUSLE models to estimate the annual water yield and soil erosion in 2050 in the Hengduan Mountain region and analyzed the variation differences in different sub-watersheds. The results indicated that, under the influence of LULC and climate change, when compared with the amount for 2020, the soil erosion in the Hengduan Mountain region in 2050 was reduced by 1.83, 3.40, and 2.91% under the TREND scenario, FOREST scenario, and CONSERVATION scenario, respectively, while the water yield decreased by 5.05, 5.37, and 5.21%, respectively. Moreover, the change in soil erosion in the study area was affected by precipitation and closely related to the precipitation intensity, and the impact of climate change on the water yield was significantly greater than that of LULC change. The spatial heterogeneity of soil erosion and water yield was obvious at the sub-watershed scale. In the future, soil erosion control should be strengthened in the northern regions, while water resource monitoring and early warning should be emphasized in the central-eastern regions. Our results provide scientific guidance for policy makers to formulate better LULC policies to achieve regional water and soil balance and sustainable management.