Cuspidal modules play a central role in the classification of simple weight modules with finite-dimensional weight spaces. In this talk, we study cuspidal \(\mathfrak{sl}_{n+1}\)-modules through the minimal finite \(W\)-algebra. Using an explicit embedding into \(U(\mathfrak{gl}_n)\), we determine the reducibility and composition factors of restrictions of finite-dimensional simple \(\mathfrak{gl}_n\)-modules, showing that their length is at most two. We then realize every simple cuspidal \(\mathfrak{sl}_{n+1}\)-module as a simple quotient of a Shen–Larsson tensor module.