Graphene-based metamaterials can generate plasma-induced transparency (PIT), offering a new approach for achieving modulators with optimal modulation performance. This study presents a multi-frequency modulator based on novel monolayer graphene structure. We utilize Coupled Mode Theory (CMT) for thorough theoretical investigations, yielding theoretical values that agree well with simulation results. Moreover, we discuss the implications of the Fermi level on PIT and the influence of graphene carrier mobility on switch modulation. The research findings illustrate the successful realization of a high-performance multi-frequency modulator by indirectly controlling the phase of the dual PIT transmission spectra through an adjustable bias voltage. Notably, at a frequency of 3.93 THz, the increasing of carrier mobility enhances the modulation depth of the modulator from 89.22 % to 97.88 % and reduces the insertion loss from 0.34 dB to 0.12 dB. Hence, our research has substantial implications for designing excellent tunable terahertz optical modulator devices and contributing to the advancement of optical communication systems and optoelectronic applications.