Rigid and flat-foldable cubes generally exhibit excellent foldable properties and significant potential for designing three-dimensional (3D) deployable structures. However, a sealed cube cannot be folded rigidly, necessitating the introduction of slits, leading to kirigami cubes. This paper aims to explore a slit-arranging technique for cubes with straight-skeleton crease patterns to create rigid and flat-foldable kirigami cubes. Considering that slits are equivalent to movable prismatic joints, rules for transforming origami cubes into equivalent mechanisms are proposed. By formulating the relationships between the selection of movable prismatic joints and the degree of freedom (DOF) of the mechanism, we propose a non-enumerative prismatic-joint-based technique for arranging slits, which significantly establish the relationships between slit arrangements and DOF based on mechanism theory. Subsequently, various slit arrangements that align with the desired DOF are obtained. Furthermore, the characteristic that the slits are closed in both fully deployed and folded configurations facilitates the construction of a bistable cube with slits sealed by elastic membranes. Comprehensive parametric studies reveal that the peak energy between stable states can be custom-designed, demonstrating significant potential for deployable aerospace structures and mechanical metamaterials. This work would greatly advance the design of 3D deployable structures.