In nature, materials such as ferroelastics and multiferroics can switch their microstructure in response to external stimuli, and this reconfiguration causes a simultaneous modulation of its material properties. Rapid prototyping technologies have enabled origami and kirigami-inspired architected materials to provide a means for designing shape-shifting structures, and here we show how multistable structures inspired by kirigami provide novel design criteria for preparing mechanical metamaterials with tunable properties. By changing the geometry of kirigami unit cells, we obtain multistable kirigami lattice structures endowed with a bistable snap-through mechanism. We demonstrate the precise control of material stiffness, along with the ability to tune this property in situ by locally and reversibly switching the unit cell configurations. We anticipate these mechanical metamaterials will provide a platform to achieve in situ tunable electrical, optical, and mechanical properties for a variety of applications in multifunctional materials, two-dimensional materials, and soft robotics.