The interest in static micromixers has increased in recent years due in part to their compact design, high area-to-volume ratio, and the absence of moving parts. The passive mixers rely mainly on the flow energy provided by the pumping system. These advantages give passive mixers an apparent edge over conventional active mixers. On the other contrary, the microflow in the static mixers typically occurs in a laminar regime at a low Reynolds number, which leads to a low mixing performance. The mixing is mainly dependent on the diffusion and the impinging of two opposite streams. To obtain a better mixing efficiency, a porous structure could be installed in the mixer's microchannel. However, a higher pressure across the mixer is to be expected. This paper introduces an innovative mixing enhancement method based on a triply periodic minimal surfaces (TPMSs) porous structure using additive manufacturing (AM) processing. The AM technology presents great potential to develop and optimize various porous matrices that could be used in advanced micro and nano-devices. Gyroid matrix has the capability to provide a better mixing performance at a moderate pressure drop compared to other TPMSs structures. Therefore, in this study, a Gyroid structure is placed in the downstream channel, aiming to boost the mixing performance. A three-dimensional mathematical model that considers conservation of mass, momentum, and species has been derived and implemented to simulate the effect of the proposed structure on the mixing index, pressure drop, and performance index. The latter is introduced as an optimization term to ensure that the optimal configuration will provide high mixing at a relatively low-pressure drop. A parametric study highlighting the impact of Reynolds and Schmidt numbers on the mixing efficiency has been conducted. The results compare the mixing index, pressure drop, and performance index of a micromixer filled with a 20% porosity Gyroid matrix with an identical plain mixer. The results indicate that the Gyroid porous structure significantly improves the mixing efficiency by almost 172%, especially at higher Reynolds numbers (Re=100 and 500). The penalty, however, is a higher pressure drop. Therefore, installing these structures requires careful consideration during the design and fabrication stage to ensure optimal performance. In addition, the results suggest that the impact of the Schmidt number on the mixing index decreases with increasing Reynolds number. The effect is negligible at Re=500. The proposed structure could be used to enhance the mixing performance of micromixers in chemical or pharmaceutical applications.