Oxide glasses have proven useful as bioactive materials, owing to their fast degradation kinetics and tunable properties. Hence, in recent years tailoring the properties of bioactive glasses through compositional design have become the subject of widespread interest for their use in medical application, e.g., tissue regeneration. Understanding the mixed alkali effect (MAE) in oxide glasses is of fundamental importance for tailoring the glass compositions to control the mobility of ions and, therefore, the glass properties that depend on it, such as ion release, glass transition temperature, and ionic conductivity. However, most of the previously designed bioactive glasses were based on trial-and-error, which is due to the complex glass structure that is nontrivial to analyze and, thus, the lack of a clear picture of the glass structure at short- and medium-range order. Accordingly, we use molecular dynamics simulations to study whether using the MAE can control the bioactivity and properties of 45S5 glass and its structural origins. We showed that the network connectivity, a structural parameter often used to access the bioactivity of silicate glasses, does not change with Na substitution with Li or K. On the contrary, the elastic moduli showed a strong dependence on the type of the modifier as they increased with increasing mean field strength. Similarly, the mobility of the glass elements was significantly affected by the type of modifier used to substitute Na. The change of the properties is further discussed and explained using changes at the short- and medium-range structure by giving evidence of previous experimental findings. Finally, we highlight the origin of the nonexistence of the MAE, the effect of the modifier on the bioactivity of the glasses, the importance of dynamical descriptors in predicting the bioactivity of oxide glasses, and we provide the necessary insights, at the atomic scale, needed for further development of bioactive glasses.