Recent studies show that structures with triply periodic minimal surfaces (TPMS) provide enhanced mechanical, acoustical, and energy abortion performance. Previously, we have shown that breaking the symmetry of the gyroid lattice—one of the most used TPMS geometry—results in the creation of directional and polarized bandgaps. Here, we focus on the effect of breaking symmetry on the effective wave speeds of the gyroid structure. We analyze the wave speeds of different asymmetric gyroid lattices using the finite element analysis approach. Our analysis shows that certain gyroid asymmetries result in the transverse waves propagating faster than the longitudinal waves in particular direction. Our research shows that breaking the symmetry leads to previously unobserved anomalous polarization of elastic waves in asymmetric gyroids.