Accretion disks around super-massive black holes (SMBH) not only power active galactic nuclei (AGNs) but also host single and binary embedded stellar-mass black holes (EBHs). The merger of these EBHs provides a promising mechanism for the excitation of some gravitational wave events observed by LIGO-Virgo. In addition to their mass and mass-ratio distribution, their hitherto enigmatic small spin-parameters (χeff) carry important clues and stringent constraints on their formation channels and evolutionary pathways. Here we show that, after each coalescence, the typical rapid spin of the merged EBHs is suppressed by their subsequent accretion of gas from a turbulent environment, due to its ability to randomize the flow’s spin orientation with respect to that of the EBHs on an eddy-turnover timescale. This theory provides supporting evidence for the prolificacy of EBH mergers and suggests that their mass growth is dominated by gas accretion rather than their coalescence in AGN disks. In addition to their contributions to the mass and χeff distribution observed by LIGO-Virgo, EBHs’ gas accretion also provides auxiliary powers to the heating of the global disk in AGNs.