Floating offshore wind turbines (FOWTs) exhibit complex motions under marine environmental loads and frequently undergo coupled oscillations across multiple degrees of freedom (DOFs). Accurate short-term motion prediction of these responses is crucial for operational safety and maintenance. To overcome the limitations of traditional “black-box” models under complex aero-hydrodynamic loads, this study proposes STL–TimesNet–NLinear, a novel physics-informed deep learning framework. The framework utilizes STL decomposition to explicitly decouple motion signals: NLinear captures non-stationary low-frequency slow drifts, while TimesNet extracts multi-periodic wave-frequency responses. The model was evaluated across different platform typologies—a 5 MW semi-submersible and a larger-scale 15 MW Spar-type platform—under various typical operational and extreme environmental conditions. Model performance was evaluated using comparative and ablation experiments. At a prediction-ahead time (PAT) of 5 s, the proposed model achieves coefficients of determination (R²) exceeding 0.95. Even at longer PATs, the R² remains above 0.90, consistently outperforming multiple benchmark models. Compared to traditional recurrent neural networks (e.g., LSTM), it decreases the Mean Absolute Error (MAE) for pitch motion under extreme sea states by 54.7% and increases the R² to 0.9573. Furthermore, the inference latency is only 2.4 ms per step. These findings confirm that the proposed STL–TimesNet–NLinear model provides fast and accurate solutions for the short-term motion response prediction of FOWTs, demonstrating valuable potential applications for enhancing the safety planning of offshore wind turbine operation and maintenance.