To clarify the rainfall-runoff response patterns in karst catchments and the mechanisms by which they are influenced by dry and wet conditions, a semi-distributed rainfall-runoff model was developed based on the V2Karst model. The developed model provides methods for calculating the consumption of epikarst water by vegetation transpiration and the convergence of groundwater flow through underground conduits. The model was applied to the Yangchang River catchment, a typical karst catchment in southwestern China, to verify its accuracy. The results show that the developed hydrological model for the karst catchment can effectively characterize the dynamic processes of discharge at the Yangchang River catchment outlet, evapotranspiration, and terrestrial water storage. During the dry season, runoff primarily comes from small fractures and dispersed infiltration in the matrix (82.1%). In the wet season, the hydrological connectivity of large fractures increases, significantly contributing to runoff. During the wet season, vegetation roots tend to consume shallow soil water (82.8% of total transpiration), whereas in the dry season, the epikarst water contributes more to vegetation transpiration, with its proportion increasing to 35.9%. Dry and wet conditions have a significant controlling effect on the hydrological connectivity of the karst catchment and the storage in different medium layers, thus affecting the flow paths and the water source for vegetation transpiration.