Poly(ε-caprolactone) (PCL) is one of the most widely used biopolymers in biomedicine for the production of scaffolds and biomaterials in tissue engineering. This is due to its characteristics as a drug carrier, as well as excellent controlled release properties compared to other biopolymers. Electrospinning is a technique often employed for manufacturing mats with this application, although chlorinated or fluorinated solvents are predominantly used, presenting high cellular toxicity. A viable alternative as a green solvent is glacial acetic acid in the preparation of electrospinning solutions. In this study, we investigated the molecular degradation via acid hydrolysis of PCL in acidic solvents (acetic acid/formic acid) and how the contact time (storage) influences the morphology of the produced structures. Solutions containing 30% by weight of PCL in acetic acid/formic acid (9:1) were prepared and stored at 35°C for up to 14 days. Subsequently, samples were tested by electrospinning to assess the resulting morphology. To analyze the acid degradation of PCL, samples were evaluated by GPC, XRD, and FTIR, revealing an approximately 50% reduction in molar mass during the solubilization process. This allowed for better chain packing, generating higher crystallinity indices, increasing from approximately 37–49%, due to the storage time of the solutions. On the other hand, it was observed that this reduction in molar mass resulted in lower molecular interactions and entanglement of the chains, reflecting in the formation of unstable Taylor cones that produced mats with various morphologies, including fibers, beaded fibers, and isolated beads. However, this degradation demonstrated an increase in water adsorption capacity, indicating exposure of hydrogen bonds from the acid hydrolysis of the ester linkage in PCL, an important feature for applications in regenerative medicine. This highlights the high potential of these hydrolyzed materials for cell anchoring applications in tissue engineering.