The long-term performance of sand–attapulgite cut-off walls in landfills is highly dependent on the permeability of the wall material. Laboratory tests show that the hydraulic conductivity of wall material decreases significantly with the increase in consolidation pressure. Therefore, to accurately estimate the hydraulic conductivity of the cut-off wall in the field, the effective stress must be calculated correctly. In this paper, the ‘modified lateral squeezing model’ is used to calculate the stress distribution of the sand–attapulgite cut-off wall, and the distribution of the hydraulic conductivity of the cut-off wall in the field is calculated based on the stress distribution of the wall and laboratory test results. The results show that the effective stress of the sand–attapulgite cut-off wall in the field increases with the increase in the depth of the wall, and the change in the hydraulic conductivity is the opposite. The effective stress of the cut-off wall is less than 100 kPa. When the wall depth is below 0.5 m, the hydraulic conductivity of the cut-off wall is less than 1.0 × 10−9 m/s. The properties of the in situ foundation soil and the width of the cut-off wall will affect the stress and hydraulic conductivity of the cut-off wall, but the influence on the hydraulic conductivity is very limited, not exceeding one time. Therefore, in the actual construction, special attention should be paid to the anti-seepage measures in the shallow part of the cut-off wall. Our findings are expected to provide a valuable reference for the application of sand–attapulgite cut-off walls in landfills.