The Surface Water and Ocean Topography (SWOT) mission has, for the first time, provided ocean observations at submesoscale resolution. While this unprecedented capability offers remarkable opportunities to resolve fine-scale oceanic structures, it also poses a fundamental challenge that how to separate oceanic motions associated with distinct dynamical regimes. In this study, a deep learning approach is trained using numerical simulations and subsequently transferred to SWOT snapshot observations to decompose sea surface height (SSH) signals associated with balanced motions (BM) and unbalanced motions (UBM). Results demonstrate that the proposed method achieves robust performance for both single-pass and an entire-cycle SWOT SSH observations. Using the extracted BM component, geostrophic sea surface velocity (SSV) are reconstructed, exhibiting strong agreement with DUACS products. These results highlight the reliability and physical plausibility of the proposed approach, which provides essential methodological support for the dynamical interpretation of high-resolution SWOT observations.