We investigate the property of the localized mixed acoustic modes lying in the interior minigap in structural defect superlattices grown away from the cubic axis of bulk materials. It is found that the localized mixed modes always appear in pairs inside each interior minigap for certain structural parameters. Furthermore, there are degeneracy points between two branches of localized mixed modes. These characteristics are markedly different from localized folded acoustic phonon modes in minigaps that occur at the center and the edge of the Brillouin zone. We also find that the interior minigap and localized mixed modes strongly depend on the growth direction of the superlattices.