The erosion of a surface by a sediment-laden flow is an inherently multiscale phenomenon which includes physical interactions covering many orders of magnitude in both length and time scales. Conforming to the nature of the problem, we propose a novel multiscale model for simulating this complex process. On the one hand, a macroscale model encompassing the whole domain of interest solves the turbulent sediment transport problem. On the other hand, a microscale model simulates the sediment impacts against the surface. A sequential multiscale strategy is used to link the sub models, such that the microscale model provides closure to the macroscale model in terms of the calculated steady state erosion rate and restitution coefficients, therefore reproducing the original coupled problem. The proposed methodology is validated against experimental data for the slurry jet erosion of a copper plate at three impingement angles. Both the global erosion rate and the erosion depth profile are predicted with mean relative errors of 18% compared to the corresponding experimental values, achieving a significant improvement over correlation-based approaches.