Huge amounts of Au and Ag are recovered from the hazardous waste lead anode slime. The conventional extraction of precious metals from lead anode slime is based on pyrometallurgical and electrolytic processes, which are seriously conditioned by the separation of harmful elements As and Sb. In this paper, an innovative and efficient oxidation–vacuum volatilization–carbon reduction process was proposed to separate and enrich Ag and Au from lead anode slime. Before vacuum volatilization, selective oxidation of the lead anode slime was performed. Then, vacuum volatilization and vacuum carbon reduction were used to obtain a gold- and silver-rich alloy. The feasibility of the process was verified experimentally and theoretically. The effects of temperature and time on vacuum volatilization separation and reduction enrichment were investigated. The experimental results showed that the Ag content in the resulting gold- and silver-rich alloy was as high as 67.58%, Au was as high as 4287 g/t, and the efficiencies for the recovery of Ag and Au from the lead anode slime were 99.25% and 99.91%, respectively. The gold- and silver-rich alloy can be directly used to produce Ag ingots. Moreover, no gas or wastewater was discharged in this process, so Ag and Au were recovered in a sustainable and cleaner manner.