We demonstrate that a phase difference between terahertz signals coupled to the gate and source and gate and drain terminals of a field effect transistor (a TeraFET) induces a plasmon-assisted DC current, which is dramatically enhanced in the vicinity of plasmonic resonances. We describe a TeraFET operation with identical radiation amplitudes at the source and drain antennas but with a phase-shift-induced asymmetry. In this regime, the TeraFET operates as a tunable resonant polarization-sensitive plasmonic spectrometer, operating in the sub-terahertz and terahertz ranges of frequencies. We also propose an effective scheme of a phase-sensitive homodyne detector operating in this phase-asymmetry mode, which allows for a dramatic enhancement of the response. These regimes can be implemented in different materials systems, including silicon. The p-diamond TeraFETs could support operation in the 200 to 600 GHz atmospheric windows, which is especially important for beyond 5G communication systems.