We report in this study the current-induced-torque excitation of acoustic and optical modes in Ta/NiFe/Ru/NiFe/Ta synthetic antiferromagnet stacks grown on SiO2/Si substrates. The two Ta layers serve as spin torque sources with the opposite polarizations in both spin currents and Oersted fields acting on their adjacent NiFe layers. This can create the odd symmetry of spatial spin torque distribution across the growth direction, allowing us to observe different spin-wave excitation efficiency from synthetic antiferromagnets excited by homogeneous torques. We analyze the torque symmetry by the in-plane angular dependence of symmetric and anti-symmetric line shape amplitudes for their resonance and confirm the parallel (perpendicular) pumping nature for the acoustic (optical) modes in our devices, which is in stark contrast to the modes excited by spatially homogeneous torques. We also present our macrospin model for this particular spin-torque excitation geometry, which excellently supports our experimental observation. Our results offer capability of controlling spin-wave excitations by local spin-torque sources, and we can explore further spin-wave control schemes based on this concept.