Recently, the information theoretic approach has been increasingly used in the robotics community as powerful quantitative measures for characterizing the dynamic coupling between the controller, the body, and the environment in embodied robots. This approach is effective and useful even if this interaction regime becomes complex and nonlinear as is often the case in soft robots. In this study, we propose a method for characterizing and visualizing the information transfer spatiotemporally through the robot’s body. This method is based on the framework called “local information transfer” proposed by Lizier et al. We extend it with the permutation-information theoretic approach, which makes it feasible for continuous time series data usually obtained in robotic platforms. To test the power of the proposed method, we performed experiments using a soft robotic arm simulator and a silicone-based soft robotic arm platform inspired by the octopus and showed that the external damage spreading is successfully and clearly visualized by the method. We also analyzed the robustness of the method to noise. Finally, we discuss future applications and possible extensions.