The periodic shedding of cloud cavitation in a nozzle orifice has a significant influence on the flow field and may have destructive effects. Most of the existing research on the shedding of cloud cavitation in an orifice is based on experimental visualization with a focus on the two-dimensional (2D) motion of the re-entrant jet and the shedding mechanism. However, the actual cloud cavitation shedding in an orifice is a complex three-dimensional (3D) process. Some limited signs of three-dimensionality and asymmetry in cylindrical orifices have been detected recently, but the 3D shedding characteristics remain unclear. In this paper, the cavitation regimes and periodic shedding process in the scaled-up nozzle orifice used by the Stanley experiment were simulated with large eddy simulation (LES). The re-entrant jet and periodic shedding mechanism, as well as, the shedding frequency, were analyzed from 2D and 3D perspectives. The main results show that the simulated cavitation regimes and the 2D periodic shedding mechanism agree fairly well with the experimental observations, but more 3D features are revealed. By analyzing the 3D shedding process and the three-dimensionality caused by the inclination of the closure line, the three-dimensional asymmetric shedding mode with phase difference π is revealed. Based upon this finding, the shedding frequency, and Strouhal number are calculated. The corresponding relationships between shedding frequencies and the frequency peaks of the power spectrum density (PSD) for pressure fluctuations are also confirmed. These results extend the understanding of the unsteady cavitating flow within nozzle orifices from 2D to 3D patterns.