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By embedding center-supported graded-circular-plates (CS-GCPs) into an elastomer, a deep-subwavelength and hydrostatic-pressure-resistant meta-absorber was designed and manufactured for sound absorption (SA) under hydrostatic pressure. The meta-absorber exhibits excellent SAs (>0.842, 0.927 on average) within 500–2000 Hz and quasi-perfect SAs (>0.94) within 500–700 Hz with a 2% thickness of the sound wavelength. The excellent SAs (0.91 on average) are verified experimentally within 1–10 kHz, and remained high (0.84 on average) under a hydrostatic pressure of 1.0 MPa. The exotic functionality arises from enriched local-dynamics by the CS-GCPs and pressure-resistance of the center-support, providing an effective solution for ultra-broadband low-frequency underwater sound control.