Cellular structures made by assembling origami attract attention because of their functions, such as auxetic behavior, anisotropic stiffness, and flexibility. This study proposes an origami cellular material inspired by BuildVoid that can switch modes between single and multiple degrees of freedom (DOF). The mechanism consists of modules with square faces repeated in two directions. By switching the folding mode of each module, the synchrony of the modules switches, which allows the switching of DOF of the whole mechanism. This paper clarifies the kinematics of the mechanism. We believe that the proposed materials with stiffness-switchable properties can be applied to robotics, adaptive materials, and programmable matter in the future.