Terahertz (THz) tunable filters have great advantages in miniaturizing integrated and multiband communication systems. Here, THz band-stop filter with switchable single/double plasmon-induced transparency (PIT) based on metal-dielectric-metal (MDM) waveguide consisting of a ring-stub cavity and two graphene ribbons (GRs) on stub sidewalls is proposed. The switchable characteristics of single and dual-PIT are investigated numerically and theoretically by the finite-difference time-domain (FDTD) and the radiating multi-oscillator theory, displaying good correspondence. The single-PIT is excited by the destructive interference between bright mode and dark mode, which possesses significant tunability of resonant frequency and transmission amplitude due to the existence of GRs. When independently regulating chemical potentials of GRs on the left and right sidewalls, the dual-PIT emerges. And the filter based on dual-PIT switches from single stopband to dual-stopband or even multi-stopband filtering. Besides, the band-stop filtering performance of the tunable PIT can be further optimized by increasing the number of ring-stub cavities. The tunable PIT in graphene-based plasmonic waveguide holds potential for THz multiband communications and subwavelength plasmonic devices, such as filters, switches, modulators.