Triply minimal surface structures of short glass fiber reinforced polyamide with different relative densities were prepared and the effects of induced anisotropy, cell topology, and relative density on the compressive properties were evaluated. Schwarz Diamond, Schoen Gyroid, and Schwarz Primitive structures were 3D printed with relative densities ranging from 0.2 to 0.4, and compression properties along the axial and lateral build directions were determined. Gipson-Ashby numerical parameters required to establish a relation between the cell topology and the compressive properties of the lattice structures were estimated. The plastic deformation and failure mechanisms were analyzed. Results revealed that the compression properties are dominated by the cell topology rather than the relative density. Besides, the present work confirmed that the compressive properties of the lattice structures fabricated with short fiber reinforcement are significantly affected by anisotropy. These structures exhibited a higher compressive modulus and lower peak compressive stress in the lateral direction, which can be attributed to the inline orientation of the short glass fibers. Schwarz Diamond proved to be the stiffest structure, followed by Schoen Gyroid and Schwarz Primitive under axial and lateral compression. Likewise, Schwarz Primitive generated low stresses compared to Schoen Gyroid and Schwarz Diamond. All cell topologies deformed in a controlled manner layer by layer, minimizing undulations in the load-bearing capacity of the structures. D and G structures compressed in the axial direction exhibited significant strain hardening and identical structures compressed in the lateral direction exhibited stable post-yield behavior with negligible undulations which is highly preferred for crashworthiness applications.