Stereo image super-resolution (stereoSR) aims to enhance the quality of super-resolution results by incorporating complementary information from an alternative view. Although current methods have shown significant advancements, they typically operate on representations at full resolution to preserve spatial details, facing challenges in accurately capturing contextual information. Simultaneously, they utilize all feature similarities to cross-fuse information from the two views, potentially disregarding the impact of irrelevant information. To overcome this problem, we propose a mixed-scale selective fusion network (MSSFNet) to preserve precise spatial details and incorporate abundant contextual information, and adaptively select and fuse most accurate features from two views to enhance the promotion of high-quality stereoSR. Specifically, we develop a mixed-scale block (MSB) that obtains contextually enriched feature representations across multiple spatial scales while preserving precise spatial details. Furthermore, to dynamically retain the most essential cross-view information, we design a selective fusion attention module (SFAM) that searches and transfers the most accurate features from another view. To learn an enriched set of local and non-local features, we introduce a fast fourier convolution block (FFCB) to explicitly integrate frequency domain knowledge. Extensive experiments show that MSSFNet achieves significant improvements over state-of-the-art approaches on both quantitative and qualitative evaluations. The code and the pre-trained models will be released at https://github.com/Tombs98/MSSFNet.