We present a mid-IR high-precision spectrometer capable of performing accurate Doppler-free measurements with absolute calibration of the optical axis and high signal-to-noise ratio. The system is based on a widely tunable mid-IR offset-free frequency comb and a Quantum-Cascade-Laser (QCL). The QCL emission frequency is offset locked to one of the comb teeth to provide absolute-frequency calibration, spectral-narrowing, and accurate fine frequency tuning. Both the comb repetition frequency and QCL-comb offset frequency can be modulated to provide, respectively, slow- and fast-frequency-calibrated scanning capabilities. The characterisation of the spectrometer is demonstrated by recording sub-Doppler saturated absorption features of the CHF ...