GPUs power modern scientific and AI applications, but their limited memory capacity restricts scalability. Buying GPUs with larger HBM is prohibitively expensive and still bounded by market limits. Existing solutions either exploit application-specific knowledge through out-of-core techniques, which lack generality, or rely on system-level page faulting, which is transparent but inefficient. We propose FRUGAL, an application-agnostic framework and methodology that reduces GPU memory footprint while sustaining high performance. FRUGAL formulates memory management as an optimization over an application’s execution graph, encompassing prefetching, kernel execution, and offloading. Using static analysis and profiling, FRUGAL applies a two-phase scheduling and migration strategy, solving an otherwise intractable optimization efficiently. Evaluations on Tiled Cholesky Decomposition, Tiled LU Decomposition, Tiny-CUDA-NN, and QuEST show that FRUGAL significantly reduces maximum GPU memory usage by 80.21%, 80.20%, 64.75% and 60.86% with only a geometric mean of 28.31% slowdown. FRUGAL allows applications to exceed hardware-imposed limits, and maintains strong performance scalability beyond existing GPU memory constraints, without additional hardware cost.