The linear oscillation of rarefied binary gas mixtures inside a two-dimensional square cavity is studied based on the McCormack model. The discrete unified gas kinetic scheme is applied to solving this problem over wide ranges of the Knudsen number and the oscillation frequency. Two typical groups of binary mixtures, i.e., the Neon–Argon (Ne–Ar) mixture with comparable molecular masses and the Helium–Xenon (He–Xe) with significant different masses are considered. The dependence of the flow characteristics and damping force on the mass ratio and the molar concentration is also investigated in detail. It is found that results of the Ne–Ar mixture with a small mass ratio have similar tendencies to those of a single gas as expected. However, the damping force of the He–Xe mixture is qualitatively different from that of a single gas. In the free-molecular and transition regimes, the molar concentration of the He–Xe mixture shows significant influence on the anti-resonant frequency. Furthermore, the anti-resonance appearing in a single gas can no longer be observed in the He–Xe mixture as the molar concentration of the light species is large in the near-continuum regime, which is helpful to avoid the damping damage for the micro-electro-mechanical devices.