The use of poly(ε-caprolactone) (PCL) for biomedical applications is well established, particularly for permanent implants, due to its slow degradation rate, suitable mechanical properties, and biocompatibility. However, the slow degradation rate of PCL limits its application for short-term and temporary biomedical applications where bioabsorbability is required. To enhance the properties of PCL and to expand its biomedical applications, we developed an approach to produce PCL membranes with tunable degradation rates, mechanical properties, and biofunctional features. Specifically, we utilized electrospinning to create fibrous PCL membranes, which were then chemically modified using potassium permanganate to alter their degradability while having minimal impact on their fibrous morphology. The effects of the chemical treatments were investigated by treating the samples for different time periods ranging from 6 to 48 h. After the 48 h treatment, the membrane degraded by losing 25% of its mass over 12 weeks in degradation studies, while maintaining its mechanical strength and exhibiting superior biofunctional features. Our results suggest that this approach for developing PCL with tailored properties could have significant potential for a range of biomedical applications.