Redox-based memristive devices are one of the most attractive candidates for future nonvolatile memory applications and neuromorphic circuits, and their performance is determined by redox processes and the corresponding oxygen-ion dynamics. In this regard, brownmillerite SrFeO has been recently introduced as a novel material platform due to its exceptional oxygen-ion transport properties for resistive-switching memory devices. However, the underlying redox processes that give rise to resistive switching remain poorly understood. By using X-ray absorption spectromicroscopy, it is demonstrated that the reversible redox-based topotactic phase transition between the insulating brownmillerite phase, SrFeO , and the conductive perovskite phase, SrFeO , gives rise to the resistive-switching properties of SrFeO memristive devices. Furthermore, it is found that the electric-field-induced phase transition spreads over a large area in (001) oriented SrFeO devices, where oxygen vacancy channels are ordered along the in-plane direction of the device. In contrast, (111)-grown SrFeO devices with out-of-plane oriented oxygen vacancy channels, reaching from the bottom to the top electrode, show a localized phase transition. These findings provide detailed insight into the resistive-switching mechanism in SrFeO -based memristive devices within the framework of metal-insulator topotactic phase transitions.