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Spatial epigenomic technologies enable simultaneous capture of spatial location and chromatin accessibility of cells within tissue slices. Identifying peaks that display spatial variation and cellular heterogeneity is the key analytic task for characterizing the spatial chromatin accessibility landscape of complex tissues. Here, we propose an efficient and iterative model, Descart, for spatially variable peaks identification based on the graph of inter-cellular correlations. Through the comprehensive benchmarking, we demonstrate the superiority of Descart in revealing cellular heterogeneity and capturing tissue structure. Utilizing the graph of inter-cellular correlations, Descart shows its potential to denoise data, identify peak modules, and detect gene-peak interactions.