To address the high operating costs caused by response delays of flexible loads and differences among parks during the coordinated operation of multi-park microgrids, a low-carbon economic operation method considering the spatiotemporally asynchronous responses of flexible loads is proposed. Firstly, a coordinated operation model of a multi-park microgrid cluster is constructed, in which wind power, photovoltaic generation, energy storage, gas turbines, and flexible loads are incorporated. Secondly, flexible loads are classified into shiftable, transferable, and curtailable loads, and their actual response delays are characterized using stochastic variables. On this basis, a low-carbon economic optimization model is established by incorporating inter-park power exchange, electricity purchase and sale with the main grid, and carbon trading. Finally, the proposed method is evaluated through a case study involving three parks. It is demonstrated that renewable energy accommodation and inter-park energy sharing can be effectively improved, while electricity purchase costs, energy storage operating costs, and gas turbine operating costs can be reduced. Compared with the scheme in which the spatiotemporally asynchronous responses of flexible loads are not considered, the total operating cost is reduced by 8.24%, and carbon emissions are further decreased.