Supercrystalline nanocomposites are nanoarchitected materials with a growing range of applications but unexplored in their structural behavior. They typically consist of organically functionalized inorganic nanoparticles arranged into periodic structures analogous to crystalline lattices, including superlattice imperfections induced by processing or mechanical loading. Although featuring a variety of promising functional properties, their lack of mechanical robustness and unknown deformation mechanisms hamper their implementation into devices. We show that supercrystalline materials react to indentation with the same deformation patterns encountered in single crystals. Supercrystals accommodate plastic deformation in the form of pile-ups, dislocations, and slip bands. These phenomena occur, at least partially, also after cross-linking of the organic ligands, which leads to a multifold strengthening of the nanocomposites. The classic shear theories of crystalline materials are found to describe well the behavior of supercrystalline nanocomposites, which result to feature an elastoplastic behavior, accompanied by compaction.