In recent years, advances in additive manufacturing have enabled the fabrication of lattice structures with remarkably small length scales. This development has prompted the topology optimization community to explore methods capable of handling a vast number of design variables. Although multi-scale topology optimization techniques have been proposed, their prohibitively high computational costs have limited their appeal in practice. As a more efficient alternative, the dehomogenization method has demonstrated promising results, particularly for compliance-based problems. In this work, we extend the findings of Allaire (2019) to address stress minimization problems, recognizing that the stress norm of a structure is a key factor in structural design. Drawing on Allaire (2004)—where the stress of rank-q laminates was minimized—we employ the homogenization method to capture the macroscopic response of a family of parameterized microstructures. Specifically, we use super-ellipsoidal holes, which have been shown in Ferrer (2022) to be optimal for stress minimization. We begin by determining the volume fraction, constitutive, and amplificator tensors for the full range of super-ellipsoidal hole parameters. Next, we optimize the macroscopic structure using standard gradient-based techniques, orienting each cell according to the principal stress components. We then dehomogenize the optimized structure by identifying a conformal map that distorts a regular grid to align with the optimal orientations. Furthermore, this work incorporates singularities in the orientation field by adding singular functions during dehomogenization. Finally, we validate the proposed methodology through several numerical examples.