Ethylenediaminetetraacetic acid (EDTA) can serve as a washing agent in the remediation of low-permeability layers contaminated by heavy metals (HMs). Therefore, batch adsorption experiments, where pure quartz (SM1) and mineral mixtures (SM2) were used as typical soil minerals (SMs) in low-permeability layers, were implemented to explore the effects of different EDTA concentrations, pH, and exogenous chemicals on the HM-SM-EDTA adsorption system. As the EDTA concentration increased, it gradually cut down the maximum Cd adsorption capacities of SM1 and SM2 from approximately 135 to 55 mg/kg and 2660 to 1453 mg/kg; and the maximum Pb adsorption capacities of SM1 and SM2 were reduced from 660 to 306 mg/kg and 19,677 to 19,262 mg/kg, respectively. When the initial mole ratio (MR = moles of HM ions/sum of moles of HM ions and EDTA) was closer to 0.5, the effect of EDTA was more effective. Additionally, EDTA worked well at pH below 7.0 and 4.0 for Cd and Pb, respectively. Low-molecular-weight organic acids (LMWOAs) affected the system mainly by bridging, complexation, adsorption site competition, and reductive dissolution. Cu2+, Fe2+ ions could significantly increase the Cd and Pb adsorption onto SM2. Notably, there were characteristic changes in mineral particles, including attachment of EDTA and microparticles, agglomeration, connection, and smoother surfaces, making the specific surface area (SSA) decrease from 16.73 to 12.59 m2/g. All findings indicated that EDTA could effectively and economically reduce the HM adsorption capacity of SMs at the reasonable MR value, contact time, and pH; EDTA reduced the HM adsorption capacity of SMs not only by complexation with HM ions but also by decreasing SSA and blocking active sites. Hence, the acquired insight from the presented study can help to promote the remediation of contaminated low-permeability layers in groundwater.