We numerically investigate the mid-infrared (MIR) supercontinuum (SC) and SC-based optical frequency comb (OFC) generations when the three optical modes (LP01, LP02, and LP12) are considered in a multimode tellurite photonic crystal fiber (MM-TPCF). The geometrical parameters of the MM-TPCF are optimized to support the multimode propagation and obtain the desired dispersion characteristics of the considered three optical modes. When the pump pulse with center wavelength λ = 2.5 μm, width T = 80 fs, and peak power P = 18 kW is coupled into the anomalous dispersion region of the LP01, LP02, and LP12 modes of the MM-TPCF, the –40-dB bandwidth of the generated MIR SCs can be up to 2.56, 1.39, and 1.12 octaves, respectively, along with good coherence. Moreover, the nonlinear dynamics of the generated SCs are analyzed. Finally, the MIR SCs-based OFCs are demonstrated when a train of 50 pulses at 1-GHz repetition rate is used as the pump source and launched into the MM-TPCF.