Abstract: To address the problems of complex coarse model construction, discontinuous responses, and low optimization efficiency in the optimization of three-dimensional microwave devices, this paper proposes a multi-strategy collaboratively accelerated mesh space mapping (MSM) method. This method is based on a coarse-mesh finite element model and constructs the coarse model through the collaboration of three key strategies. First, structure sharpening is employed to approximately simplify complex boundaries such as rounded corners and tuning screws, significantly reducing the number of mesh elements and the complexity of geometric modeling. Second, a radial basis function–based mesh morphing method is adopted to maintain the continuity and differentiability of the coarse model response under geometric parameter perturbations. Third, sensitivity analysis is used for parameter screening to extract the main correlated variables between the coarse and fine models, thereby reducing the mapping dimensionality and the number of required training samples. Based on the above strategies, an integrated “sharpening–morphing–screening” coarse model generation mechanism is constructed and embedded into the MSM optimization process. Using a fourth-order tunable cavity filter as an example, the proposed method is validated: under the premise of maintaining optimization accuracy, the total optimization time is reduced from 14.4 hours to 1.5 hours, achieving nearly 90% improvement in efficiency. This method is applicable to optimization tasks with multiple tuning structures, high-dimensional parameter spaces, and strongly discontinuous responses, providing a feasible approach and engineering path for building automated and low-cost electromagnetic optimization systems.