Stencil computation is one of the fundamental computing patterns in many application domains such as scientific computing and image processing. While there are promising studies that accelerate stencils on FPGAs, there lacks an automated acceleration framework to systematically explore both spatial and temporal parallelisms for iterative stencils that could be either computation-bound or memory-bound. In this article, we present SASA, a scalable and automatic stencil acceleration framework on modern HBM-based FPGAs. SASA takes the high-level stencil DSL and FPGA platform as inputs, automatically exploits the best spatial and temporal parallelism configuration based on our accurate analytical model, and generates the optimized FPGA design with the best parallelism configuration in TAPA high-level synthesis C++ as well as its corresponding host code. Compared to state-of-the-art automatic stencil acceleration framework SODA that only exploits temporal parallelism, SASA achieves an average speedup of 3.41× and up to 15.73× speedup on the HBM-based Xilinx Alveo U280 FPGA board for a wide range of stencil kernels.