U(VI) and tetracycline (TC) in hospital wastewater pose serious threats to human health and the environment. In this study, agricultural corn straw residue was utilized as a precursor for biochar, and biochar-supported nano-hydroxyapatite (nHAP) adsorbents (CSPCs) were synthesized at various ratios. These CSPCs were employed for the removal of U(VI) and TC in both one-component and two-component systems. In the one-component system, the adsorption capacity of the material was related to the ratio of nHAP to biomass, and the maximum adsorption capacities of CSPC-1 (nHAP/biomass = 1/1) for U(VI) and TC were 724.63 mg g−1 and 15.06 mg g−1, respectively. The XPS and XRD results confirmed that biochar promoted the dissolution and precipitation of U(VI) by nHAP, which stabilized the adsorption of U(VI) by CSPC-1. In the two-component system, the complexation strength of U(VI) and TC had a significant effect on the adsorption of both. At pH < 3.0, U(VI) inhibited the adsorption of TC, whereas TC enhanced the adsorption of U(VI). However, at pH > 4.0, the adsorption of U(VI) and TC were mutually reinforcing. At pH = 5.0, TC inhibited the adsorption of U(VI) only when the concentration of TC was significantly greater than that of U(VI). Combined with the systematic analysis of the FTIR, XPS and Raman spectroscopic results, these results suggest that these phenomena can be attributed to the complexation-bridging interactions between U(VI) and TC and their competition for adsorption sites.