The propulsion of a liquid indium-tin microdroplet by nanosecond-pulse laser impact is experimentally investigated. We capture the physics of the droplet propulsion in a scaling law that accurately describes the plasma-imparted momentum transfer over nearly three decades of pulse energy, enabling the optimization of the laser-droplet coupling. The subsequent deformation of the droplet is described by an analytical model that accounts for the droplet's propulsion velocity and the liquid properties. Comparing our findings to those from vaporization-accelerated millimeter-sized water droplets, we demonstrate that the fluid-dynamic response of laser-impacted droplets is scalable and decoupled from the propulsion mechanism. By contrast, the physics behind the propulsion of liquid-metal droplets differs from that of water. It is studied here in detail and under industrially relevant conditions as found in next-generation nanolithography machines.