Electron beam irradiation by transmission electron microscopy (TEM) is a common and effective method for post-synthesis defect engineering in two-dimensional transition metal dichalcogenides (TMDs). Combining density functional theory (DFT) with relativistic scattering theory, we simulate the generation of such defects in monolayer group-VI TMDs, MoS2, WS2, MoSe2, and WSe2, focusing on two fundamental TEM-induced atomic displacement processes: chalcogen sputtering and chalcogen vacancy migration. Our calculations show that the activation energies of chalcogen sputtering depend primarily on the chalcogen species, and are smaller in selenides than in sulfides. Meanwhile, chalcogen vacancy migration activation energies hinge on the transition metal species, being smaller in TMDs containing Mo. Incorporating these energies into a relativistic, temperature-dependent cross section, we predict that, with appropriate TEM energies and temperatures, one can induce migrations in all four group-VI TMDs without simultaneously producing vacancies at a significant rate. This can allow for the formation of complicated defects and extended patterns, and thus, for the controlled manipulation of TMD crystals for targeted functionality, without the risk of substantial collateral damage.