Mechanical properties of materials can be altered significantly by the ancient art of kirigami. We study the mechanical properties of atomically thin kirigami membranes of MoS2 using molecular dynamics simulations. Nanoindentation simulations are performed to study the mechanical response of rectangular and hexagonal kirigami structures. Dramatic changes are observed in the ductility of monolayer kirigami MoS2 compared with those of a pristine MoS2 monolayer. Load-displacement curves of kirigami structures exhibit negligible hysteresis, and kirigami structures display remarkable elastic recovery upon unloading. Defects formed at the edges and corners of kirigami structures play an important role in the mechanical response of the membranes.