The montmorillonite@iron oxide@silver (MMT@Fe3O4@Ag) nanocomposite, which is recyclable and exhibits high catalytic activity, was evaluated for the degradation of methyl yellow (MY), a carcinogenic azo dye. For this purpose, MMT@Fe3O4 was first synthesized via the coprecipitation method and then Ag was doped to MMT@Fe3O4 via the chemical reduction method. MMT, MMT@Fe3O4, and MMT@Fe3O4@Ag were characterized by various techniques including scanning electron microscopy, Fourier transform infrared spectroscopy, X-ray diffraction, vibrating sample magnetometer, and thermal gravimetric analysis. The results illustrated that MMT@Fe3O4@Ag exhibited a higher catalytic ability than MMT@Fe3O4 toward decolorization of MY with a degradation efficiency of 100% in 10 min at pH 7.1 in the presence of sodium borohydride (NaBH4). Further, some parameters like the amount of NaBH4, initial dye concentration, and pH were also studied to determine optimum reaction conditions. MMT@Fe3O4@Ag could be easily separated and recycled from the reaction medium using an external magnet. Thus, the Ag-doped MMT@Fe3O4 nanocomposite proved to have good catalytic activity, high MY degradation rate and reusability, and easy separation and simple synthesis method. These properties make it a promising catalyst for the treatment of wastewater containing organic pollutants. In addition, artificial neural network (ANN) simulation, which is a mathematical model with an artificial intelligence algorithm, was used for the degradation process. This model was evaluated with the parameters used in the experiment as the input and output layers. Last, the degradation of MY with the synthesized catalyst into different products was demonstrated by high-performance liquid chromatography (HPLC) analysis.