We　study　static　behavior　and　mechanical　cooling　of　a　dissipative　optomechanical　system　by　considering　a　phase-controlled　coupling　strength.　We　find　that　the　static　displacement　of　the　mechanical　oscillator　vanishes　when　the　dissipative　coupling　strength　becomes　purely　imaginary,　while　a　real　coupling　strength　gives　rise　to　a　driving　power-dependent　static　mechanical　displacement.　The　absence　of　static　displacement　sustains　the　resonance　linewidth　of　the　effective　Fabry-Pérot　cavity　and　guarantees　the　approximation　of　a　linear　dissipative　coupling.　In　this　case,　we　show　that　the　membrane　can　be　cooled　from　the　cryogenic　temperature　to　its　quantum　ground　state　outside　the　resolved-sideband　limit　with　a　moderately　strong　driving　operating　at　the　red-detuned　regime,　where　the　optomechanical　cooling　rate　can　be　competitive　with　typical　schemes　that　utilize　a　real　coupling　strength　and　a　blue-detuned　laser　drive.　The　dissipative　optomechanical　system　with　a　phase-controlled　coupling　strength　offers　the　flexibility　to　investigate　fundamental　optomechanical　effects　and　may　find　potential　applications　in　high-sensitive　position　transduction.　©　2025　American　Physical　Society.