In the last years, additive manufacturing has allowed to build lattice structures with impressive small length scale. This breakthrough has forced the topology optimization community to propose new techniques that are able to consider an immense number of design variables. Some attempts include multi-scale topology optimization techniques, however its prohibitive computational cost has made this technique less attractive from a computational point of view. As an alternative, the dehomogenization method has recently shown very promising results in terms of performance and computational cost [1] for compliance examples. In this work, we extend the results of [1] to the stress minimization problems since the stress norm of a structure is key aspect in structural design. Following work [2] where the stress of rank-q laminates where minimized, we use the homogenization method to obtain the macroscopic response of a proposed family of parametrized microstructures, in this case super-ellipsoidal holes, which have been proved to be optimal for stress minimization problems in [3]. The fraction volume, constitutive and amplificator tensors are first obtained for all the possible values of the super-ellipsoidal hole parameters. Then, the macroscopic structure is optimized using standard gradient based methods and orienting the cell following the principal stress components. Finally, the structure is dehomogenized finding a conformal map that deforms a regular grid that coincides with the optimal orientation. In this work, we also consider singularities in the orientation field by adding singular functions in the dehomogenization process. We finally present several numerical examples to validate the proposed methodology.