Visual reasoning may require models to interpret images and videos and respond to implicit text queries across diverse output formats, from pixel-level segmentation masks to natural language descriptions. Existing approaches rely on supervised fine-tuning with task-specific architectures. For example, reasoning segmentation, grounding, summarization, and visual question answering each demand distinct model designs and training, preventing unified solutions and limiting cross-task and cross-modality generalization. Hence, we propose DT-R1, a reinforcement learning framework that trains large language models to construct digital twin representations of complex multi-modal visual inputs and then reason over these high-level representations as a unified approach to visual reasoning. Specifically, we train DT-R1 using GRPO with a novel reward that validates both structural integrity and output accuracy. Evaluations in six visual reasoning benchmarks, covering two modalities and four task types, demonstrate that DT-R1 consistently achieves improvements over state-of-the-art task-specific models. DT-R1 opens a new direction where visual reasoning emerges from reinforcement learning with digital twin representations.