Carbon fiber-reinforced composites (CFRC) are pivotal in advanced engineering applications due to their exceptional mechanical properties. A deep understanding of CFRC behavior under mechanical loading is essential for optimizing performance in demanding applications such as aerospace structures. While traditional Finite Element Method (FEM) simulations, including advanced techniques like Interface-enriched Generalized FEM (IGFEM), offer valuable insights, they can struggle with computational efficiency. Existing data-driven surrogate models partially address these challenges by predicting propagated damage or stress-strain behavior but fail to comprehensively capture the evolution of stress and damage throughout the entire deformation history, including crack initiation and propagation. This study proposes a novel auto-regressive composite U-Net deep learning model to simultaneously predict stress and damage fields during CFRC deformation. By leveraging the U-Net architecture's ability to capture spatial features and integrate macro- and micro-scale phenomena, the proposed model overcomes key limitations of prior approaches. The model achieves high accuracy in predicting evolution of stress and damage distribution within the microstructure of a CFRC under unidirectional strain, offering a speed-up of over 60 times compared to IGFEM.