Mechanical properties of powder bed fusion processed unalloyed copper are reported majorly in the as-fabricated condition, and the effect of post-processes, common to additive manufacturing, is not well documented. In this study, mechanical properties of unalloyed copper processed by electron beam powder bed fusion are characterized via room temperature quasi-static uniaxial tensile test and Vickers microhardness. Tensile samples were extracted both perpendicular and parallel to the build direction and assigned to three different conditions: as-fabricated, hot isostatic pressing (HIP), and vacuum annealing. In the as-fabricated condition, the highest UTS and lowest elongation were obtained in the samples oriented perpendicular to the build direction. These were observed to have clear trends between sample orientation caused primarily by the interdependencies between the epitaxial columnar grain morphology and dislocation movement during the tensile test. Texture was insignificant in the as-fabricated condition, and its effect on the mechanical properties was outweighed by the orientation anisotropy. The fractographs revealed a ductile mode of failure with varying dimple sizes where more shallow and finely spaced dimples were observed in the samples oriented perpendicular to the build direction. EDS maps reveal that grain boundary oxides coalesce and grow in HIP and vacuum-annealed specimens which are seen inside the ductile dimples and contribute to their increased ductility. Overall, for the post-process parameters chosen in this study, HIP was observed to slightly increase the sample’s density while vacuum annealing reduced the oxygen content in the specimens.