This study delves into the axial responses of Schwarz Primitive (SP) structures. Emphasising on bearing capacity, force distribution, cracking phenomena, load-displacement curve and energy absorption. Discrete element method (DEM) is adopted to analyse the axial load-bearing behaviour and fracture mechanics of Main SP and Secondary SP structures under various unit cell configurations after validated by experimental tests. The results indicates that despite sharing the same 1/8th cell structure, the axially-loaded behaviours of the Main SP and Secondary SP structures are not identical, particularly in scenarios involving a large unit cell size and a small number of unit cells. The Main SP structures display an axial load-bearing behaviour that is largely unaffected by variations in the number of unit cells along the x and y axes, while Secondary SP structures show a more pronounced improvement in average strength and energy absorption capacity when the number of unit cells increases. Main SP structures offer superior axial load-bearing capabilities and energy absorption efficiency, which is a significant consideration for their application in scenarios demanding high structural integrity. This distinction underlines the importance of tailored design and selection of SP configurations based on specific engineering requirements.