To reliably assess the rupture risk of the aorta, along with the hazardousness of cardiovascular diseases and other extreme conditions or the effect of possible treatments, it is necessary to understand the influence of damage mechanisms along with the frequency and rate of mechanical loads. In particular, hypobaric hypoxia, an oxygen deficiency in the organism due to its low atmospheric partial pressure, is reported to alter the mechanical properties of blood vessels. In this work, we characterized the passive mechanical response of the aorta, seeking to capture the influence of hypoxia on their elastic, damage, and viscoelastic properties under ex-vivo conditions. The mechanical behavior of the aortic wall is described using an anisotropic hyperelastic model including two fiber families with asymmetric dispersion, along with an anisotropic damage model and an orthotropic viscoelastic model based on a reverse multiplicative decomposition of the deformation gradient. The constitutive model was experimentally calibrated from uniaxial-relaxation and biaxial-tensile test results, previously performed on thoracic aorta samples of guinea pigs. A group of guinea pigs subjected to hypoxia was contrasted with a normoxic (control) group. Cyclic-load stages of uniaxial tests were used to assess dissipation. Once the constitutive model was implemented and calibrated, its performance was evaluated via the numerical simulation of a bulge pressurization test to estimate energy dissipation and pressure associated with the onset of damage. Results indicated that hypoxia does not alter the visco-hyperelastic or damage behavior of the aorta. Besides, the pressure delivered by bulge-test simulations at the onset of damage on collagen fibers was representative of an arterial hypertensive condition.