Water resource pollution is a major global challenge that poses a serious threat to human health and the environment. In this study, glutaraldehyde was used to cross-link polyethyleneimine (PEI) with yeast and starch. The PEI-modified yeast was attached to the yam starch adsorption gel using the gel properties of starch to prepare a novel starch-based composite adsorbent material (NH2(Gl)-YSA@SZ410). Owing to its porous interconnected structure, the material exhibited optimal adsorption performance, wettability, and mechanical properties. NH2(Gl)-YSA@SZ410 could remove Congo red (CR), Cu2+, and coexisting pollutants (CR and Cu2+ mixture) from solutions. At 308 K, in single CR- or Cu2+-contaminated solutions, the maximum adsorption capacities were 293.52 and 50.34 mg/g, respectively, whereas in the binary-pollutant system, the maximum adsorption capacities were 363.15 and 149.50 mg/g, respectively. Additionally, an in-depth study of single-pollutant and binary-pollutant systems was conducted using adsorption kinetics, isotherms, and adsorption mechanisms. Theoretical calculations indicated that CR and Cu2+ interacted with NH2(Gl)-YSA@SZ410 composite materials through forces such as hydrogen bonding and electrostatic interactions. Furthermore, NH2(Gl)-YSA@SZ410 exhibited excellent stability and practicality. The adsorbent can be effectively applied to wastewater containing both heavy metals and dyes, offering novel ideas for biobased adsorbents.