Inspired by the success of large language models (LLMs), there is growing research interest in developing LLMs in the medical domain to assist clinicians. However, for hospitals, using closed-source commercial LLMs involves privacy issues, and developing open-source public LLMs requires large-scale computational resources, which are usually limited, especially in resource-efficient regions and low-income countries. We propose an open-source Small Language and Vision Assistant (SLaVA-CXR) that can be used for Chest X-Ray report automation. To efficiently train a small assistant, we first propose the Re$^3$Training method, which simulates the cognitive development of radiologists and optimizes the model in the Recognition, Reasoning, and Reporting training manner. Then, we introduce a data synthesis method, RADEX, which can generate a high-quality and diverse training corpus with privacy regulation compliance. The extensive experiments show that our SLaVA-CXR built on a 2.7B backbone not only outperforms but also achieves 6 times faster inference efficiency than previous state-of-the-art larger models.