The development of an environmentally friendly scavenger with an outstanding ability to eliminate IACDCs from molasses-based distillery wastewater is essential for the safety of aquatic ecosystems and organisms. By combining polyamine co-modified shaddock peel cellulose (SPC) and graphene oxide (GO), a multistage porous aerogel (i.e., CP-GO/SPA) was constructed for the highly effective capture of IACDCs. CP-GO/SPA exhibited a surprisingly high IACDC adsorption capacity (1157 mg/g, which was 1.5–100 times that of previously reported ones). It also had an ultrafast adsorption mass transfer (AMT) rate. Advanced AMT-resistance models reveal that the capture on active site is the main AMT resistance, whereas liquid-film and pore diffusion are quite fast. CP-GO/SPA exhibited excellent reusability (>90% IACDC removal efficiency after six cycles) and considerable potential for industrial applications (i.e., treatment of actual wastewater by fixed-bed adsorption). The polyamine co-modified SPC and GO endowed CP-GO/SPA with substantial amine groups and high affinity for water, as validated by advanced molecular dynamics simulations. These features are extremely conducive for capturing electronegative and water-soluble IACDCs. A series of characterizations and multiple quantum chemical theory calculations (including ETP, ALIE, FMOs, IGM, and HIS analyses) further revealed the adsorption mechanisms from a molecular perspective. The IACDC capture by CP-GO/SPA resulted from charge, electron sharing, and van der Waals interactions. However, charge interactions played a dominant role. The optimal capture configurations were visualized at the molecular level, and the H-bond donor–acceptor relationship was determined. The IACDCs act as H-bond acceptors in a diverse range of capture configurations.