Arsenic (As), cadmium (Cd), and copper (Cu) are the primary inorganic pollutants commonly found in contaminated soils. The simultaneous stabilization of the three elements is a preferred approach for mixture-contaminated soils which has received extensive research attention. However, few studies have focused on the immobilization efficiency of a single amendment on the three elements. In this study, phosphate, red mud, and biochar were used to remediate As (237.8 mg kg−1), Cd (28.72 mg kg−1), and Cu (366.5 mg kg−1) co-contaminated soil using a 180-day incubation study. The BCR (European Community Bureau of Reference) extraction method, NH4H2PO4−extractable As, and diethylenetriamine penta-acetic acid (DTPA)−extractable Cd and Cu were analyzed at different time intervals. The results indicated that the application of red mud and biochar significantly reduced soil DTPA−Cd and Cu concentrations during the incubation, while the decrease in soil NH4H2PO4−As was much less than that of soil DTPA−Cd and Cu. After 180 days of incubation, the concentrations of NH4H2PO4−As in red mud and biochar treatments decreased by 2.15~7.89% and 3.01~9.63%, respectively. Unlike red mud and biochar, phosphate significantly reduced the concentration of soil DTPA−Cd and Cu, but failed to lower that of As. The BCR extraction method confirmed that red mud and biochar addition increased the reducible fraction of As due to the surface complexes of As with Fe oxide. Canonical correspondence analysis (CCA) demonstrated that soil pH in addition to available As, Cd, and Cu concentrations were the primary factors in driving the changes in soil enzymatic activity. Soil pH showed positive correlation with soil urease and catalase activities, while negative correlation was observed between soil-available As, Cd, and Cu, and soil enzyme activities. This study revealed that it is difficult to simultaneously and significantly reduce the bioavailabilities of soil As, Cd, and Cu using one amendment. Further research on modifying these amendments or applying combined amendments will be conducted, in order to develop an efficient method for simultaneously immobilizing As, Cd, and Cu.