Smoothed Particle Hydrodynamics (SPH) is a mesh-free, fully Lagrangian method widely used for simulating complex fluid flows involving free surfaces, large deformations, and multi-physics interactions. Despite its flexibility, the computational efficiency of SPH is often limited by time integration constraints. In explicit formulations, stability requirements arising from different physical processes, such as acoustic wave propagation, particle advection, viscous diffusion, and heat conduction, are typically combined into a single global time step. This single-rate strategy forces all components of the governing equations to be advanced at the most restrictive time scale, leading to significant inefficiencies when pronounced time-scale separations are present. In this work, we apply a general multi-rate time integration scheme to weakly compressible SPH that overcomes this limitation while preserving stability and accuracy. The governing equations are consistently partitioned into advection, acoustic, viscous, and thermal contributions, each of which is integrated using a time step adapted to its characteristic time scale. Fast processes are subcycled relative to slower ones, while intermediate states are reconstructed through interpolation strategies that ensure coherent coupling between the different physical components. The performance and accuracy of the method are assessed using several benchmark problems, including the Taylor–Green vortex, a three-dimensional dambreak, thermal Couette flow, and pore-scale flow through periodic porous media. In all cases, the multi-rate scheme reproduces analytical solutions and experimental reference data with accuracy comparable to that of conventional single-rate integration. Significant computational speed-ups ranging from approximately 1.7× to over 4×, depending on the degree of time-scale separation, are achieved without compromising solution quality. The proposed multi-rate time integration scheme therefore provides an efficient and robust alternative to single-rate approaches, particularly for multi-physics SPH simulations.