This paper investigates the mechanical behavior of additive manufactured Triply Periodic Minimal Surface (TPMS) structures, such as Gyroid, Schwarz Diamond and Schwarz Primitive. Fused Filament Fabrication (FFF) technique was utilized in order to fabricate lattice structures with different relative densities, at 10%, 20% and 30%, using Polylactic acid (PLA). The test specimens were formed by structural TPMS unit cells and they were tested under quasi-static compression. A finite element analysis (FEA) was performed in order to predict their stress-strain behavior and compare with the experimental results. The results revealed that each architecture influences the mechanical properties of the structure differently depending on the impact of size effect. The structures were designed as sandwich structures (with a top and bottom plate) to avoid significant deterioration of the mechanical behavior, due to the size effect and this was achieved at high relative densities. The Schwarz Diamond structure demonstrated the highest mechanical strength compared with the other architectures, while the Gyroid structure also revealed a similar mechanical performance. In addition, Schwarz Primitive structure showed increased energy absorption especially during plastic deformation. The overall results revealed that the integrity of the mechanical properties of the studied TPMS FFF printed structures deteriorates, as the relative density of the structures decreases.