This paper addresses the challenge of Satellite Video Super-Resolution (SVSR) by proposing a practical Blind SVSR algorithm (BSVSR). Unlike existing methods that assume fixed and known degradation, such as bicubic downsampling, BSVSR focuses on blind SR to handle multiple and unknown degradations. The key innovation is the consideration of pixel-wise blur levels in a coarse-to-fine manner, using multi-scale deformable convolution and multi-scale deformable attention to aggregate temporal redundancy and sharp cues. A pyramid spatial transformation module is also introduced to adjust the solution space of the sharp mid-feature, enhancing its adaptability to various degradations. Extensive experiments on simulated and real-world satellite videos demonstrate that BSVSR outperforms state-of-the-art non-blind and blind SR models in terms of both quantitative metrics and visual quality. The code for BSVSR is available at <https://github.com/XY-boy/Blind-Satellite-VSR>.This paper addresses the challenge of Satellite Video Super-Resolution (SVSR) by proposing a practical Blind SVSR algorithm (BSVSR). Unlike existing methods that assume fixed and known degradation, such as bicubic downsampling, BSVSR focuses on blind SR to handle multiple and unknown degradations. The key innovation is the consideration of pixel-wise blur levels in a coarse-to-fine manner, using multi-scale deformable convolution and multi-scale deformable attention to aggregate temporal redundancy and sharp cues. A pyramid spatial transformation module is also introduced to adjust the solution space of the sharp mid-feature, enhancing its adaptability to various degradations. Extensive experiments on simulated and real-world satellite videos demonstrate that BSVSR outperforms state-of-the-art non-blind and blind SR models in terms of both quantitative metrics and visual quality. The code for BSVSR is available at <https://github.com/XY-boy/Blind-Satellite-VSR>.