The engineering of optomechanical systems has exploded over the past decades, with many geometries and applications arising from the coupling of light with mechanical motion. The modulation of electromagnetic radiation in the terahertz (THz) frequency range through optomechanical systems is no exception to this research effort. However, some fundamental modulation capabilities for THz communications and/or high-speed data processing applications are yet to be established. Here, we demonstrate a THz time-domain derivative spectrometer based on a piezoelectric micromachined (PM) device. Insertion of the PM device into the THz beam path provides reference modulation for the lock-in detection unit, which in turn provides access to the nth-order derivative information of the incoming THz signal. Strikingly, the integration of the recorded derived signal leads to a recovered reference signal with an equivalent or even better signal-to-noise ratio, opening the door to a new type of highly sensitive THz measurements in the time domain.