Heterodyne terahertz spectrometers are highly in demand for space explorations and astrophysics studies. A conventional heterodyne terahertz spectrometer consists of a terahertz mixer that mixes a received terahertz signal with a local oscillator signal to generate an intermediate frequency signal in the radio frequency (RF) range, where it can be easily processed and detected by RF electronics. Schottky diode mixers, superconductor-insulator-superconductor (SIS) mixers and hot electron bolometer (HEB) mixers are the most commonly used mixers in conventional heterodyne terahertz spectrometers. While conventional heterodyne terahertz spectrometers offer high spectral resolution and high detection sensitivity levels at cryogenic temperatures, their dynamic range and bandwidth are limited by the low radiation power of existing terahertz local oscillators and narrow bandwidth of existing terahertz mixers. To address these limitations, we present a novel approach for heterodyne terahertz spectrometry based on plasmonic photomixing. The presented design replaces terahertz mixer and local oscillator of conventional heterodyne terahertz spectrometers with a plasmonic photomixer pumped by an optical local oscillator. The optical local oscillator consists of two wavelength-tunable continuous-wave optical sources with a terahertz frequency difference. As a result, the spectrometry bandwidth and dynamic range of the presented heterodyne spectrometer is not limited by radiation frequency and power restrictions of conventional terahertz sources. We demonstrate a proof-of-concept terahertz spectrometer with more than 90 dB dynamic range and 1 THz spectrometry bandwidth.