On-demand metal droplet ejection is a critical technical branch in industrial electronics. Among them, high temperature and surface tension are the mainly limited factors affecting the single droplet ejection of hot-melt metal. To this end, this article proposed a waveform optimization scheme based on a piezoelectric micro-jet device (PMJD) actuated by a piezoelectric stack and a flexible hinge amplifier for liquid metal. The structure and operation principle of the PMJD is presented and analyzed. The numerical simulation model for hot-melt metal is established; the ejection mechanism and boundary condition of metal droplet are analyzed in detail by a direct fluid-thermal-structure interactions numerical method, which reveals two operation modes of metal droplet ejection under trapezoidal driving waveform. The driving waveform for the PMJD is designed and optimized to allow metal droplets to be ejected, and the variation of the initial velocity and shape of droplets are also analyzed based on the designed waveform. Furthermore, the critical value of satellite droplets generation with fracture of liquid bridge is discussed by simulation, and the optimized waveforms can also be used to suppress satellite droplets.