High-feed cutting, such as that used in the machining of high-precision large-pitch thread, is expected to find wide application in the fabrication of key parts of large-scale equipment. The static and dynamic precision of a large-scale press is directly affected by the machining accuracy and surface quality of the large-pitch thread. We propose a new time-varying dynamic model of a large-pitch external thread subjected to a tridirectional moving load and an algorithm for vibration offset calculation. The model has also been validated experimentally and has enabled us to study in detail the phenomenon of chatter in the machining processes. Prediction models for dimensional error and surface morphology, which take into account the vibration offset of the workpiece, are proposed and the results obtained from them agree well with the experimental observations. Finally, the effects of vibration of the workpiece alone and the effects of coupled vibration of the cutter and workpiece on machining accuracy and surface quality are analyzed using the prediction models. Results indicate that there are differences in dimensional accuracy and surface morphology between the left and right flanks of the thread. Furthermore, the degree of variation in dimensional error is more obvious in the left flank than in the right; the wave curve density associated with the machined surface morphology of the left flank is large and the spacing of the wave curves is small. The results also show that the dimensional error in the intermediate stage is larger than those in the initial and the end stages. The study builds a theoretical basis for suppressing workpiece vibration during the cutting process and provides technical assistance for ensuring high-quality machining with a long stroke of the thread, improving machining accuracy, and making sure of consistent surface quality.