Cardiovascular disease, arteriosclerosis, is characterized by the thickening of blood vessel (arteries) walls restricting blood flow and is a global health problem. One treatment option is a surgical procedure utilizing an autologous or synthetic vascular graft to bypass or replace the diseased arterial segment. The goal of this study was to fabricate and mechanically characterize near field electrospun bioresorbable vascular grafts with a fibrous architecture that mimics the arterial extracellular matrix. Polydioxanone vascular constructs with circumferential fiber alignment angles of 15°/75° and 30°/60° (0° representing circumferential fiber alignment) were fabricated using a custom built near-field electrospinning (NFES) system. The vascular construct mechanical properties were compared to the saphenous vein (SV) and internal mammary artery (IMA) through longitudinal and circumferential uniaxial mechanical testing, suture retention, and burst pressure evaluations. The results demonstrated that the 15°/75° templates were closest to mimicking the native vessel target properties as compared to the 30°/60°; however, neither of the vascular template designs achieved or exceeded all the target values. For the ultimate tensile strength, both the constructs met the SV value on the circumferential axis (2.61 MPa) and the IMA value on the longitudinal axis (4.3 MPa). In terms of suture retention, the 15°/75° template was the only construct that was in the IMA and SV targeted range of 138–200 gf. Finally, the burst pressure testing results indicated that neither of the vascular constructs achieved the level of the SV or IMA (1600–3196 mmHg), however, the 15° constructs were within the lower error of the SV. In conclusion, with further design modifications, NFES constructs have demonstrated promise as small-diameter vascular grafts by mimicking native arterial architecture and mechanical properties.