Balancing economic scheduling and low-carbon operation in power systems while effectively leveraging the potential of source-load coordination is critical for current power system optimization. Then, a source-load coordinated low-carbon economic scheduling method considering carbon intensity-electricity price joint response mechanism was proposed. The low-carbon operational characteristics of carbon capture power plants under integrated flexible operation modes and the load regulation principles of demand response were elaborated. Additionally, their complementarity in low-carbon operation was analyzed, and a coordinated operational framework for carbon capture power plants and demand response was established. By allocating partial carbon responsibility to the load side using carbon emission flow theory, a carbon intensity-electricity price joint response model was proposed to enhance the carbon reduction capability of the load side. With the goal of minimizing system operating cost, based on the tiered carbon trading mechanism and combined with the proposed source-load coordinated operation framework, a two-stage low-carbon economic scheduling model was developed to achieve coordinated source-load optimization. Comparative analysis of multiple scenarios based on a modified IEEE 39-bus system demonstrated that the proposed method could reduce system carbon emissions by 15% and decrease comprehensive operating costs by 4%, validating its coordinated optimization in both economic and low-carbon performance.