Understanding cellular mechanosensitivity and its tissue-level manifestations pose fundamental questions, with far-reaching implications. We study the self-organization of vascular networks formed by cells embedded in 3D biomaterials under external mechanical driving forces. We show that under oscillatory stretching of the biomaterial, the newly formed network exhibits orientational order perpendicular to the stretching direction, independently of the geometric aspect ratio. A 2D theory of non-interacting single cells explains this observation in terms of the stored elastic energy transferred to the network for cell-embedded biomaterials that feature a vanishing effective Poisson’s ratio, which we directly verify. We further show that under static stretching, the vascular networks exhibit orientational order parallel to the stretching direction due to deformation-induced anisotropy of the biomaterial polymer network. Finally, successive static and oscillatory stretching reveals a competition between the two mechanosensitive mechanisms. These results support the 2D non-interacting theory and its application to the tissue level, and provide insights regarding the emergence of orientational order in self-organizing tissues.