In recent years, carbon-based two-dimensional (2D) materials have gained popularity as the carriers of various anticancer therapy drugs, which could reduce the crucial side effects by directly applying the drugs to the intended tumor cells. In this study, through first-principles density functional theory simulations, we have investigated the adsorption properties of a famous cancer chemotherapy drug called mercaptopurine (MC) on a 2D γ-graphyne (GYN) monolayer. Analyzing the geometric and electronic properties, we can summarize that the MC interaction with the pristine GYN is weak, with a small adsorption energy of -0.15 eV, which is too low for potential applications. Therefore, we have decorated the GYN monolayer with biocompatible metals such as Al, Ag, and Cu to trigger the adsorption capacity. The Al- and Cu-decorated GYN offered improved adsorption towards MC compared to the pristine case. The drug release from these metal-decorated systems was examined by creating an acidic environment. In addition, the desorption temperature of the drug from the system was also evaluated using ab initio molecular dynamics simulations. The calculations demonstrated that the Al-decorated GYN is a potential vehicle for MC drug delivery because of the favourable adsorption energy of -0.63 eV, charge transfer of 0.17e and desorption temperature above 270 K. The current research will stimulate the investigation of other low-dimensional carbon materials for drug-delivery applications.