Because their topological structures have certain crystallographic symmetry, there is anisotropy in triply periodic minimal surface (TPMS) porous structures. Anisotropy can affect the mechanical properties of porous structures; thus, it is necessary to research the anisotropy of TPMS structures. In this study, based on quaternionic three-dimensional rotation, TPMS structures were rotated around three crystal directions: [100], [110], and [111]. The mechanical anisotropy behaviors of TPMS porous structures, including gyroid, diamond, primitive, and I-graph-wrapped package (IWP) graph surfaces, were studied through finite element analysis (FEA). The FEA results show that the anisotropy of the IWP structure with rotation in the [110] direction was the most significant, and its relative elastic modulus increased by 275.33% when the IWP was rotated 60° in the [110] direction. These results indicate that the uniaxial compression performance of TPMS structures can be significantly improved by using structural anisotropy. However, it should be noted that due to this significant anisotropy, the performance of such structures will significantly decrease in specific directions. For example, after the primitive structure was rotated 60° in the [111] and [110] directions, its relative elastic modulus decreased by 72.66% and 77.6%, respectively. Therefore, it was necessary to reasonably consider the bearing capacity in fragile directions under complex working conditions. Based on the anisotropy of TPMS, gradient TPMS structures with three rotation angles were designed and manufactured using selective laser melting technology. The compressive results show that multi-peaks appeared in the primitive structure with gradient rotation in the [111] direction from 0° to 40°, and step-by-step behaviors were observed in the IWP structure with gradient rotation in the [110] direction from 0° to 60°. This result shows that the yielding platform can be enhanced using gradient rotation designation based on the anisotropy of TPMS porous structures.