Populating the exoplanet mass-radius diagram in order to identify the underlying relationship that governs planet composition is driving an interdisciplinary effort within the exoplanet community. The discovery of hot super-Earths & mdash;a high-temperature, short-period subset of the super-Earth planet population & mdash;has presented many unresolved questions concerning the formation, evolution, and composition of rocky planets. We report the discovery of a transiting, ultra-short-period hot super-Earth orbiting TOI-1075 (TIC 351601843), a nearby (d = 61.4 pc) late-K/early-M-dwarf star, using data from the Transiting Exoplanet Survey Satellite. The newly discovered planet has a radius of 1.791(-0.081)(+0.116) R-circle plus and an orbital period of 0.605 day (14.5 hr). We precisely measure the planet mass to be 9.95(-1.30) (+1.36) M-circle plus using radial velocity measurements obtained with the Planet Finder Spectrograph mounted on the Magellan II telescope. Our radial velocity data also show a long-term trend, suggesting an additional planet in the system. While TOI-1075 b is expected to have a substantial H/He atmosphere given its size relative to the radius gap, its high density ( 9.32(-1.85)(+2.05) g cm(-3)) is likely inconsistent with this possibility. We explore TOI-1075 b's location relative to the M-dwarf radius valley, evaluate the planet's prospects for atmospheric characterization, and discuss potential planet formation mechanisms. Studying the TOI -1075 system in the broader context of ultra-short-period planetary systems is necessary for testing planet formation and evolution theories and density-enhancing mechanisms and for future atmospheric and surface characterization studies via emission spectroscopy with the JWST.