Stencil computation is one of the most important kernels in various scientific computing. Nowadays, most Stencil-driven scientific computing still relies heavily on supercomputers, suffering from expensive access, poor scalability, and duplicated optimizations.This paper proposes Tetris, the first system for highperformance Stencil on heterogeneous CPU+GPU, towards democratizing Stencil-driven scientific computing on Cloud. In Tetris, polymorphic tiling tetrominoes are first proposed to bridge different hardware architectures and various application contexts with a perfect spatial and temporal tessellation automatically. Tetris is contributed by three main components: (1) Underlying hardware characteristics are first captured to achieve a sophisticated Pattern Mapping by register-level tetrominoes;(2) An efficient Locality Enhancer is first presented for data reuse on spatial and temporal dimensions simultaneously by cache/SMEM-level tetrominoes; (3) A novel Concurrent Scheduler is first designed to exploit the full potential of on-cloud memory and computing power by memory-level tetrominoes. Tetris is orthogonal to (and complements) the optimizations or deployments for a wide variety of emerging and legacy scientific computing applications. Results of thermal diffusion simulation demonstrate that the performance is improved by 29.6×, reducing time cost from day to hour, while preserving the original accuracy.