Recent progress in 4D representations, such as Dynamic NeRF and 4D Gaussian Splatting (4DGS), has enabled dynamic 4D scene reconstruction. However, text-driven 4D scene editing remains under-explored due to the challenge of ensuring both multi-view and temporal consistency across space and time during editing. Existing studies rely on 2D diffusion models that edit frames independently, often causing motion distortion, geometric drift, and incomplete editing. We introduce Dynamic-eDiTor, a training-free text-driven 4D editing framework leveraging Multimodal Diffusion Transformer (MM-DiT) and 4DGS. This mechanism consists of Spatio-Temporal Sub-Grid Attention (STGA) for locally consistent cross-view and temporal fusion, and Context Token Propagation (CTP) for global propagation via token inheritance and optical-flow-guided token replacement. Together, these components allow Dynamic-eDiTor to perform seamless, globally consistent multi-view video without additional training and directly optimize pre-trained source 4DGS. Extensive experiments on multi-view video dataset DyNeRF demonstrate that our method achieves superior editing fidelity and both multi-view and temporal consistency prior approaches. Project page for results and code: https://di-lee.github.io/dynamic-eDiTor/