Aimed at low-frequency noise in aerospace applications, a micro-perforated plate (MPP) and a triply periodic minimal Surface (TPMS) was combined as a MPP–TPMS sandwich structure. This structure achieves efficient mid-to-low frequency sound absorption while maintaining advantages in lightweight design and compactness. The Primitive structure in the TPMS structure was selected as the structural core material, and a Helmholtz resonator array can be formed by designing a perforated plate-cavity unit. Based on microperforated plate sound absorption theory and Johnson-Champoux-Allard equivalent fluid theory, a theoretical sound absorption model of the MPP–Primitive sandwich structure was established to explore the coupling effect of local resonance effect and thermal viscous dissipation mechanism in sound wave attenuation. Samples were fabricated by fused deposition modeling (FDM) technology. The effects of MPP, unit cell size of Primitive, cavity thickness, and MPP aperture on the acoustic properties of the sandwich structure were systematically investigated through acoustic impedance tube tests and finite element simulations. The results demonstrate that the combination of MPP and TPMS activates the sound absorption mechanism of the Helmholtz resonance cavity and greatly improves the sound absorption characteristics, and the sound absorption frequency band moves towards the lowfrequency region, and the sound absorption peak is close to 1. Increasing the size of the Primitive effectively expands the volume of the resonance cavity, reduces the low-frequency acoustic impedance, and enhances the acoustic impedance matching with low-frequency sound waves, thereby improving the absorption efficiency of low-frequency sound waves. Reducing the MPP’s aperture and increasing the surface acoustic resistance of the structure effectively broadens the bandwidth of the sound absorption peak, greatly improving the peak value of the sound absorption and migrating it to low frequencies. Increasing the thickness of the primitive cavity, extending the sound wave propagation path, and migrating the Helmholtz resonance peak to low frequencies by enhancing viscous dissipation and heat conduction effects. This work provides support for the design of sub-wavelength low-frequency sound-absorbing MPP–TPMS composite sound-absorbing metamaterials.