The folding and cutting of materials provides a facile means to tune mechanical and physical characteristics. Kirigami, the Japanese art of paper cutting, has demonstrated that the inclusion of cut patterns enables complex 3D structures from 2D sheets, elastic softening, and large deformations under external loading. These features have primarily been achieved through either the bending of beams defined by cuts or the rotation of hinges between beams. However, the synergistic coupling of these deformation modes has not been explored. Here we show that the inclusion of minor cuts into patterned structures defined by major cuts integrates hinge rotations with beam bending and generates significant tunability, further reducing stiffness by a factor of 30 and increasing the deformability by a factor of 2. Experimental results are validated by theoretical predictions in which the addition of minor cuts of various lengths to major cuts exhibits a similar response to varying boundary conditions and beam shapes. We present generalized equations to provide criteria for designing optimized kirigami structures in various applications. This concept of hybrid structures is demonstrated with highly stretchable conductors, which show nearly constant resistance with strains up to ~400 %, and rapid magnetoactive soft actuators, which elongates to 330 % in ~0.1 s with a maximum strain rate of 10,000 % s-1. This work can enable substantial variations in stiffness and deformation of functional materials for applications in soft robotics, stretchable electronics, and human-machine interfaces.