High harmonic generation (HHG) in the terahertz (THz) regime is an emerging field that has already provided new insights into fundamental low-energy processes in Dirac materials and high-T_C superconductors. Here, we demonstrate THz harmonic generation across the Mott insulator-metal transition in rare-earth nickelates (RNiO₃, R = rare-earth atom). The THz harmonic signal shows distinct characteristics in the three different accessible phases: the intensity of harmonics increases upon cooling in both the low-temperature antiferromagnetic (AFM) insulating and high-temperature paramagnetic (PM) metallic phases, while this trend is reversed in the intermediate PM insulating phase. Using single- and two-band Hubbard models, we find different dominant origins of the THz harmonics in different phases: strong spin-charge and orbital-charge coupling in the AFM insulating phase, intraband currents from renormalized quasiparticles with temperature-dependent scattering rate in the PM metallic phase, and the reduction of the charge carrier density due to the opening of the Mott gap in the PM insulating phase. These results and mechanisms significantly differ from those observed upon excitation in the optical regime. Our study lays the foundation for THz HHG physics in Mott and other strongly correlated systems and offers design principles for efficient THz HHG from these systems.