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This work demonstrates how the geometric and topological characteristics of substructures within heterogeneous materials can be employed to tailor the mechanical responses of soft crystals under large strains. The large deformation mechanical behaviors of elastomeric composites possessing long-range crystalline order are examined using both experiments on 3D printed prototype materials and precisely matched numerical simulations. The deformation mechanisms at small and large strains were elucidated for six sets of morphologies: dispersed-particles on each of the simple cubic, body-centered cubic or facecentered cubic lattices, and their bi-continuous counterparts. Comparison of results for the six types of morphologies revealed that the topological connectivity of dissimilar domains is of critical importance for tailoring the macroscopic mechanical properties and the mechanical anisotropy.