This paper describes the vibroacoustic behavior of sandwich panels with a novel core topology made from 2-dimensionally gradient auxetic hexagonal honeycombs. The 2D gradient core enables a tailoring of localized mechanical properties of the sandwich structure in different regions of the panel. A homogenized finite element modeling has been used to initially determine the mechanical properties of the structures. The natural frequencies and the radiated sound power level of the sandwich plate with the homogenized properties have been calculated and verified with those obtained from a full-scale detailed model of the sandwich structure. The geometry of the 2-dimensionally gradient auxetic core has been then optimized using two different techniques in order to minimize the radiated sound power level over the frequency range of 0 to 200 Hz. The optimized design of the 2-D gradient core shows a remarkable reduction of the radiated sound power level for the sandwich structure when taking into account the mass of the panels. The results of this study provide new insights about the vibroacoustic behavior of hexagonal auxetic sandwich structures with complex core geometry.