Three series of soda-lime glasses doped with varying contents of Mg, Si3N4, or a combination of both were synthesized using laser melting in less than 3 min. The addition of these dopants resulted in notable changes in the structural and thermal properties of the glass. Both IR and Raman spectra indicated that the silicate network primarily consisted of Q3 units, with significant amounts of Q2 and Q4 units present in most samples. In the Mg-doped series, strong depolymerization was observed, evidenced by an increase in Q2 units and a decrease in Q4 units. Conversely, increasing the Si content led to greater polymerization, with Q2 units being replaced by Q4 units. The series containing both Mg and Si exhibited features influenced by both elements, showing increases in Q2, Q3, and Q4 units. The glass transition temperature (Tg) increased with the addition of Mg and Si across all series. This increase was attributed to the strong cross-linking effect of Mg-O bonds and the increased polymerization with higher glass-forming ion content. However, a decrease in glass stability was observed, particularly in Mg-containing samples, due to Mg acting as a nucleation agent and promoting crystallization of the silicate structure. In contrast, Si did not introduce new nucleation sites, thus contributing to the structural integrity of the glass network. The findings underscore the potential of laser melting as an effective method for tailoring the properties of glasses.