A monolayer graphene-based tunable triple-band terahertz plasmon device with superior sensing and slow light performance is proposed in this work. A very obvious dual PIT phenomenon is observed by adjusting the device structure. Then, the transmission curves and electric field distributions of the long- and short-graphene band at the three transmission windows are analyzed, to further investigate the mechanism of the bright mode and the dark mode of this structure. Afterward, the comparison between the theoretical data from the coupled-mode theory (CMT) and the simulation results of finite difference time domain (FDTD) shows that they are in excellent agreement with each other. In addition, the effective refractive indices of the real and imaginary parts at different Fermi energy levels are analyzed. The effective refractive indices are linearly related to the Fermi energy level. In this research, it is found that the phase of the electromagnetic wave fluctuates strongly at the transmission window. With the increase of the Fermi energy level, the peak frequency of the group refractive index peak value increases. When the Fermi energy level is at 1.1 eV, the peak value of the group refractive index reaches 327.1. In order to study the sensing effect of this device in more depth, various refractive indices of the medium are tested. Based on these results it can be seen that the device has excellent sensing performance. Its sensitivity and figure of merit (FOM) reach up to 1.442 THz/RIU and 39.6921, respectively. Compared with the traditional structure, this structure can regulate the Fermi energy levels very conveniently by applying a voltage, in order to modulate the resonant frequency of the dual PIT. The findings in this study are expected to lay a theoretical foundation and provide a design reference for potential applications in fields such as slow light technology and sensing.