Solid particulate and water hydrodynamic cavitation flow (SPW-HCF), one solid-liquid-vapor with phase change three-phase flow, often appears in many different engineering fields. SPW-HCF has both desirable and problematic effects. Solid particulate mean diameter has significant effects on hydrodynamic cavitation intensity. In this study, one new coupled numerical method of vapor, liquid, and solid was built. SPW-HCF with the mean diameter increasing from 0.0015 mm to 0.070 mm in a nozzle was numerically simulated. Effects of solid particulate mean diameter on hydrodynamic cavitation intensity were evaluated. Vapor contents of SPW-HCF and pure water hydrodynamic cavitation flow (PW-HCF) were compared to build the laws and variations of slip velocity, turbulent kinetic energy, and Saffman lift force were analyzed to reveal the mechanisms. The results indicated that for the laws, all SPW-HCF vapor contents were greater than those in PW-HCF. Solid particulates promoted cavitation evolution. The concentration promotion scope decreased as mean diameter increased. For the mechanisms, maximal and absolute minimal slip velocities were higher in SPW-HCF than those in PW-HCF. Moreover, maximal and minimal turbulent kinetic energies of SPW-HCF were higher than those in PW-HCF. Corresponding mixture kinetic energies were higher than those in PW-HCF. With the synergetic effects of slip velocity and turbulent kinetic energy, pressure had significant decrease to promote SPW-HCF development. They were primary factors. The magnitude of Saffman lift force calculated in SPW-HCF was relatively small. The effects on the decrease of pressure were minute. SPW-HCF evolution was affected weakly by this force. It can be considered as a secondary influence factor. The investigation results could provide the references to solve corresponding practical engineering problems.