The minimal surface structure is a continuous and smooth porous structure. It has the advantages of low density, high intensity, and excellent energy absorption capability. This paper has studied the mechanical properties and energy absorption characteristics of the minimal surface prepared by additive manufacturing process using nylon PA12. First, using the parametric modelling method, three kinds of minimal surface porous structures (G-surface, P-surface, and D-surface) with the same volume fraction of 20% are designed. The corresponding minimal surface structures are manufactured with Multi Jet Fusion (MJF) additive manufacturing technology. The mechanical response and energy absorption characteristics of different minimal surface structures are then analyzed by combining quasi-static compression tests and numerical simulations. For the mechanical response, it is found that the three kinds of minimal surface structures show better load-bearing capacities compared with the traditional BCC lattice structure. In detail, the nominal stresses of the three minimal surface structures (G-surface, P-surface, and D-surface) are 4.0 MPa, 2.1 MPa, and 4.75 MPa, respectively. The nominal stress value of the BCC lattice structure under the same volume is 2.0 MPa. It is clear that all values of the three minimal surface structures are significantly higher than that of the BCC lattice structure. For the study of energy absorption, the energy absorption per unit volume is used as one of key parameter to evaluate the energy absorption characteristic of the porous structure. The results indicate that the values of the energy absorption per unit volume for the three minimal surface structures (G-surface, P-surface, and D-surface) are all higher than that of the BCC lattice structure. The energy absorption per unit volume for the three minimal surface structures can approximately reach 7, 4, and 8 times that of the BCC lattice structure. In conclusion, the minimal surface structure can show excellent characteristics of mechanical property and energy absorption and has extensive application prospects in the fields of aerospace, automotive industry, and machinery.