Lattice metamaterials based on three-period minimum surface (TPMS) are an effective means to achieve lightweight and high-strength materials which are widely used in various fields such as aerospace and ships. However, its vibration and noise reduction, and damping properties have not been fully studied. Therefore, in this study, the TPMS structures with parameterization were designed by the method of surface migration, and the TPMS structures with high forming quality was manufactured by laser powder bed fusion (LPBF). The mechanical properties and energy absorption characteristics of the beam and TPMS structures were studied and compared by quasi-static compression. The modal shapes of the beam lattice structures and TPMS structures were obtained by the free modal analysis, and the damping properties of two structures were obtained by modal tests. For the two structures after heat treatment with the same porosity of 70%, the yield strength of the beam lattice structure reaches 40.76 MPa, elastic modulus is 20.38 GPa, the energy absorption value is 32.23 MJ·m^-3, the damping ratio is 0.52%. The yield strength, elastic modulus, energy absorption value, and damping ratio of the TPMS structure are 50.74 MPa, 25.37 GPa, 47.34 MJ·m^-3, and 0.99%, respectively. The results show that TPMS structures exhibit more excellent mechanical properties and energy absorption, better damping performance, and obvious advantages in structural load and vibration and noise reduction compared with the beam lattice structures under the same porosity.