Parallel multigrid methods are widely used as preconditioners for solving large-scale sparse linear systems. Most multigrids rely on general sparse matrix formats, which prevent them from achieving optimal performance. There is an emerging trend towards semi-structured multigrids that balance flexibility with performance. However, existing libraries often fall short in terms of speed and scalability for semi-structured problems. To address these limitations, we have designed and implemented Semi-StructMG. It employs multi-dimensional coarsening to reduce complexity and simplify communication patterns. It also considers the special role of inter-block connections in smoothers and triple-matrix products to improve convergence under large-scale parallelism. We evaluated Semi-StructMG using two benchmark problems and four real-world applications from petroleum reservoir simulation, ship manufacturing, numerical weather prediction, and ocean modeling. Compared to \textit{hypre}’s multigrids, Semi-StructMG achieves the fastest time-to-solution across all cases, with average speedups of 5.97x, 15.2x, and 3.85x over SSAMG, Split, and BoomerAMG, respectively. Additionally, Semi-StructMG significantly improves both strong and weak scaling efficiencies in all tests.