Kirigami, i.e. paper cutting is nowadays widely investigated to design the mechanical structure that can be transformed with unique and programmable performances. When it is transformed, the components of the kirigami are also reconfigured and then provide tunable polarization-sensitive electromagnetic responses. In this study, we present a design of stretchable kirigami mechanical metamaterial (SKMM) with dual electromagnetically induced transparency (EIT) resonances. The proposed two designs of SKMM show two dual EIT resonances at 0.905 THz, 0.975 THz, and 0.449 THz, 0.558 THz, which can be switched to 0.964 THz, 1.042 THz and 0.433 THz, 0.532 THz by rotating kirigami cells in predestinated orientations, respectively. During the continuous modulations of transmission spectra by increasing the stretching force, the characteristics of resonant spectra maintain excellent with their corresponding averaged Q-factors as 33.19, 21.59 and 4.87, 17.31, respectively. The EIT resonances originating from the bright-bright mode could be explained with multipole scattering theory along with the three-dimensional schematic illustrations. These results prove the proposed SKMM possesses promising applications in slow light, optical data computing, quantum information technology, and sensing fields.