This paper presents a numerical study on the hopper discharging of widely polydisperse particles. It focuses on the effects of particle size distributions (PSDs) in the form of the log-normal distribution of the number (nPSD) and volume (vPSD) of particle constituents. In doing so, a recent GPU-DEM model suitable for large-scale simulations is adopted. The numerical results show that the mass discharge rate reduces with increasing nPSD spread but becomes larger at a wider vPSD spread. The discharging process is analyzed in terms of packing density, coordination number, velocities, and force network. It is observed that the packing density equally increases for both PSDs as the spread grows, whereas the coordination of the mixture reduces. Thus, a negative correlation between coordination and packing density is consistently observed. With increasing nPSD spread, the particle vertical velocities drop significantly, which are nearly unchanged for wider vPSDs. The particle-scale analysis is also extended to energy dissipation. The analysis reveals that the effect of PSD on the mass discharge rate is mainly attributed to the relative importance of different energy dissipation mechanisms. Irrespective of PSD type, the friction energy dissipation decreases with widening PSD, which becomes more pronounced near the outlet. In contrast, as the spread becomes wider, the collision dissipation near the outlet turns more important for nPSD but decreases for vPSD. These results account for different trends of discharge rates with respect to PSD type.