Traditional channel acquisition faces significant limitations due to ideal model assumptions and scalability challenges. A novel environment-aware paradigm, known as channel twinning, tackles these issues by constructing radio propagation environment semantics using a data-driven approach. In the spotlight of channel twinning technology, a radio map is recognized as an effective region-specific model for learning the spatial distribution of channel information. However, most studies focus on static channel map construction, with only a few collecting numerous channel samples and using deep learning for radio map prediction. In this paper, we develop a novel dynamic radio map twinning framework with a substantially small dataset. Specifically, we present an innovative approach that employs dynamic mode decomposition (DMD) to model the evolution of the dynamic channel gain map as a dynamical system. We first interpret dynamic channel gain maps as spatio-temporal video stream data. The coarse-grained and fine-grained evolving modes are extracted from the stream data using a new ensemble DMD (Ens-DMD) algorithm. To mitigate the impact of noisy data, we design a median-based threshold mask technique to filter the noise artifacts of the twin maps. With the proposed DMD-based radio map twinning framework, numerical results are provided to demonstrate the low-complexity reproduction and evolution of the channel gain maps. Furthermore, we consider four radio map twin performance metrics to confirm the superiority of our framework compared to the baselines.