We study the effects of heavy hole-light hole (HH-LH) mixing on fine-structure and polarization properties of neutral excitons ( X-0) confined in single GaAs/AlGaAs quantum dots (QDs) under the application of anisotropic biaxial stress. In the large HH-LH mixing regime, these properties are substantially different from the usually observed properties in the case of small or no mixing. By varying the applied stress, the mixing in the initially strain-free QDs changes from similar to 0 to similar to 70% and an anomalous anticrossing of the X-0 bright states is observed. The latter is attributed to stress-induced rotation of the in-plane principal axis of the QD confinement potential. We show that the analysis of free-excitonic emission of bulk GaAs surrounding the QDs not only allows estimation of the stress and mixing in the QDs, but also provides the quantum-confinement-induced HH-LH splitting of the as-grown QDs.