During nuclear waste vitrification, loss of sodium (Na) and boron (B) occurs, as these elements are highly volatile at high temperatures, which affects the properties of the glass products. Moreover, the evaporation of volatile nuclides (Cs and Tc) occurs together with that of Na and B, which may cause environmental hazards. Thus far, only a few studies have focused on the volatilization of Na and B from nuclear waste glass and loss-related effects on glass properties. In this study, we investigated the volatilization behaviors of Na and B from a simulated high-level waste glass as functions of heating temperature and dwelling duration, and evaluated the effects of Na and B loss on the glass structure and thermal stability. The results showed that volatilization of Na occurs predominantly through the diffusion-controlled process at a temperature range of 950 °C to 1100 °C, and owing to its higher frequency factor, Na diffuses and volatilizes at a faster rate than that of B. Volatilization of B occurs by both a diffusion-controlled process from bulk to the surface and a chemical reaction process on the surface. Based on the data obtained regarding the composition of Na and B and structure of the glass, a hypothetical model was proposed to explain the volatilization behaviors of Na and B from a structural viewpoint. As the loss of Na and B increases, the amount of BO4− reduces, whereas the amount of BO3 increases; finally, the Si-O network becomes more polymerized and has less thermal stability, resulting in the crystallization of the glass at elevated temperatures. These results would serve as the basis to estimate the amount of Na and B loss and the properties of the glass melt during nuclear waste vitrification, especially in melter idling.