Current multimodal large language models (MLLMs) still face significant challenges in complex visual tasks (e.g., spatial understanding, fine-grained perception). Prior methods have tried to incorporate visual reasoning, however, they fail to leverage attention correction with spatial cues to iteratively refine their focus on prompt-relevant regions. In this paper, we introduce SIFThinker, a spatially-aware "think-with-images" framework that mimics human visual perception. Specifically, SIFThinker enables attention correcting and image region focusing by interleaving depth-enhanced bounding boxes and natural language. Our contributions are twofold: First, we introduce a reverse-expansion-forward-inference strategy that facilitates the generation of interleaved image-text chains of thought for process-level supervision, which in turn leads to the construction of the SIF-50K dataset. Besides, we propose GRPO-SIF, a reinforced training paradigm that integrates depth-informed visual grounding into a unified reasoning pipeline, teaching the model to dynamically correct and focus on prompt-relevant regions. Extensive experiments demonstrate that SIFThinker outperforms state-of-the-art methods in spatial understanding and fine-grained visual perception, while maintaining strong general capabilities, highlighting the effectiveness of our method.