In this study, a tunable graphene plasmonic filter and a two-channel demultiplexer are proposed, simulated, and analyzed in the mid-infrared (MIR) region. We discuss the optical transmission spectra of the proposed cross-shaped resonator and the two-channel demultiplexer. The transmission spectra of the proposed MIR resonator are tunable by change of its dimensional parameters and the Fermi energy of the graphene. Our proposed structures have a single mode in the wavelength range of 5-12 µm. The minimum full width at half maximum (FWHM) and the maximum transmission ratio of the proposed resonator respectively reached 220 nm and 55%. Simulations are performed by use of three-dimensional finite-difference time-domain (3D-FDTD) method. Coupled mode theory (CMT) is used to investigate the structure theoretically. The numerical and the theoretical results are in good agreement. The performance of the proposed two-channel demultiplexer is investigated based on its crosstalk. The minimum value of crosstalk reaches −48.30 dB. Our proposed structures are capable of providing sub-wavelength confinement of light waves, useful in applications in MIR region.