Octave-spanning frequency comb generation in the deep mid-infrared (>5.5 μm) typically requires a high pump power, which is challenging because of the limited power of narrow linewidth lasers at long wavelengths. We propose twofold dispersion engineering for a Ge-on-Si microcavity to enable both dispersion flattening and dispersion hybridization over a wide band from 3.5 to 10 μm. A two-octave mode-locked Kerr frequency comb can be generated from 2.3 to 10.2 μm, with a pump power as low as 180 mW. It has been shown that dispersion flattening greatly enhances the spectral broadening of the generated comb, whereas dispersion hybridization improves its spectral flatness.