Infectious respiratory diseases have long been a serious public health issue, with airborne transmission via close person-to-person contact being the main infection route. Coughing episodes are an eruptive source of virus-laden droplets that increase the infection risk of susceptible individuals. In this study, the droplet generation process during a coughing event was reproduced using the Eulerian wall film (EWF) model, and the absorption/expulsion of droplets was tracked using the discrete phase model (DPM). A realistic numerical model that included the oral cavity with teeth features and the respiratory system from the throat to the first bifurcation was developed. A coughing flow profile simulated the flow patterns of a single coughing episode. The EWF and DPM models were coupled to predict the droplet formation, generation, absorption, and exhalation processes. The results showed that a large droplet number concentration was generated at the beginning of the coughing event, with the peak concentration coinciding with the peak cough rate. Analysis of the droplet site of origin showed that large amounts of droplets were generated in the oral cavity and teeth surface, followed by the caudal region of the respiratory system. The size of the expelled droplets was 0.25–24 μm, with the peak concentration at 4–8 μm. This study significantly contributes to the realm on the site of origin and localized number concentration of droplets after a coughing episode. It can facilitate studies on infection risk assessment, droplet dispersion, and droplet generation mechanisms from other sneezing or phonation activities.