The effects of strain rate, size (height × width), and pre-existing crack length on the mechanical response of polycaprolactone electrospun membranes were investigated by tension tests conducted at room temperature. In particular, tensile tests were performed with three different strain rates for strain rate effect tests, seven different geometries for elucidating the size effect, and three different initial notch lengths for crack growth experiments. The electrospun membranes were produced by the electrospinning technique using a polycaprolactone solution prepared in 1, 1, 1, 3, 3, 3-hexafluoro-2-propanol as the solvent. Scanning electron microscopy was utilized to show the continuous fiber structure without bead formation. The average fiber diameter was calculated as 1.113 ± 0.270 μm by using scanning electron microscopy images of the membranes. The chemical structure of polycaprolactone was analyzed by Fourier transform infrared spectroscopy, and the toxicity and cell viability of the electrospun membranes were shown by CellTiter 96® Aqueous One Solution Cell Proliferation Assay (MTS test). It was observed that the ultimate tensile strength and Young’s modulus decreased, and the elongation at failure value increased as the strain rate decreased from 10−1 to 10−3 s−1. Besides, positive strain rate sensitivity was observed on the mechanical response of electrospun polycaprolactone membranes. Moreover, the dependency of mechanical response on the size geometry has been well studied, and the optimum height and width combinations were specified. Also, crack growth was studied in terms of both macroscopic and microstructural deformation mechanisms and it is observed that individual fiber deformations and interactions are highly effective on the mechanical behavior and also propagation of the crack. Consequently, in this study, the size and strain rate effects and crack growth on the mechanical response of electrospun polycaprolactone membranes have been investigated extensively, and the results presented herein constitute an essential guideline for the usage of polycaprolactone electrospun membranes at different loading scenarios.