In this work, we develop a machine-learning interatomic potential for WxMo1−x random alloys. The potential is trained using the Gaussian approximation potential framework and density functional theory data produced by the Vienna ab initio simulation package. The potential focuses on properties such as elastic properties, melting, and point defects for the whole range of WxMo1−x compositions. Moreover, we use all-electron density functional theory data to fit an adjusted Ziegler-Biersack-Littmarck potential for the short-range repulsive interaction. We use the potential to investigate the effect of alloying on the threshold displacement energies and find a significant dependence on the local chemical environment and element of the primary recoiling atom.