Engineering materials that simultaneously achieve efficient low-frequency sound absorption and high load-bearing capacity remain challenging to develop. Inspired by the lightweight and mechanically robust architecture of cuttlebone, this study proposes a bioinspired labyrinthine metamaterial (BLM) that integrates superior compressive properties with designable sound-absorption capabilities. By incorporating asymmetric sinusoidal walls into a labyrinthine configuration, the proposed structure enhances both acoustic energy dissipation and mechanical stability. An analytical acoustic-impedance model, numerical simulations, and experimental measurements were employed to investigate its acoustic and mechanical performance. The BLM achieves near-perfect sound absorption at 258.5 Hz, with an experimentally measured absorption coefficient of 1.00 and a subwavelength thickness of approximately λ/45. Meanwhile, the interconnected asymmetric walls improve stress distribution and buckling resistance, resulting in a specific compressive strength of 32.97 MPa·cm³/g, which is 3.26 times that of a conventional labyrinthine metamaterial. Furthermore, a compact broadband design strategy based on length-graded cavities and dual-pore configurations achieves average sound absorption coefficients of approximately 0.80 across 490–660 Hz and 620–810 Hz. These findings demonstrate a bioinspired approach to developing lightweight multifunctional metamaterials that combine superior mechanical performance with tunable low-frequency and broadband sound absorption, offering promising opportunities for advanced engineering applications.