Bi-metallic nanoparticles (NPs) have appeared to be more efficient as antimicrobials than mono-metallic NPs. The fungus Aspergillus terreus-mediated synthesis of bi-metallic Ag-Cu NPs was optimized using response surface methodology (RSM) to reach the maximum yield of NPs. The optimal conditions were validated using ANOVA. The optimal conditions were 1.5 mM total metal (Ag + Cu) concentration, 1.25 mg fungal biomass, 350 W microwave power, and 15 min reaction time. The structure and shape of the synthesized NPs (mostly 20–30 nm) were characterized using several analytical tools. The biological activities of the synthesized NPs were assessed by studying their antioxidant, antibacterial, and cytotoxic activity in different NP concentrations. A dose-dependent response was observed in each test. Bi-metallic Ag-Cu NPs inhibited three clinically relevant human pathogens: Klebsiella pneumoniae, Enterobacter cloacae, and Pseudomonas aeruginosa. Escherichia coli, Enterococcus faecalis, and Staphylococcus aureus were inhibited less. The DPPH and hydrogen peroxide scavenging activities of the NPs were high, reaching 90% scavenging. Ag-Cu NPs could be studied as antimicrobials in different applications. The optimization procedure using statistical analyses was successful in improving the yield of nanoparticles.