Cloud microphysics controls precipitation, latent heating, and the radiative properties of clouds, and it remains a source of complexity in atmospheric models. The super-droplet method is a Lagrangian, particle-based approach that evolves per-particle attributes and makes no assumptions about the shape of the size distribution. Its fidelity comes at a higher computational cost than that of bulk schemes. We present a scalable, portable implementation of the super-droplet method for cold, mixed-phase microphysics in the Energy Research and Forecasting (ERF) code. It includes ice processes such as freezing, deposition, sublimation, riming, aggregation, and a gradual heat-balance melting that retains the mixed-phase state of each particle. The implementation is portable by construction across NVIDIA, AMD, and Intel graphics processing units through the AMReX framework, and we demonstrate it on NVIDIA and AMD hardware. We verify the method against theory and published benchmarks. We then simulate a three-dimensional deep-convection case based on the GARP Atlantic Tropical Experiment (GATE), where the method resolves the ice-particle morphology and the phase structure of the mature cloud without predefined hydrometeor categories. The method scales efficiently to 512 graphics processing units on the deep-convection case with more than a billion super-droplets, and we report and compare the computational cost of the microphysical processes.