<p>The influence of undercooling (Δ<i>T</i>) on the glass formation of TiCu-based glass-forming alloys was systematically investigated by modulating the Cu mold temperature upon arc-suction casting. Δ<i>T</i> of the undercooled liquids changed from 545 to 321&#xa0;K depending on the mold temperature, which induced a significant change in the microstructure of alloys from a bulk metallic glass (BMG) composite containing crystals to a monolithic BMG. The unexpected enhancement in the glass-forming ability of the TiCu-based BMGs was mainly related to the evolution of the local chemical heterogeneity (LCH) of the glassy phases. The LCH in BMGs became more pronounced with increasing Δ<i>T</i>, and nuclei formed in Cu-rich regions. On the other hand, the LCH in the glassy phases gradually weakened under small Δ<i>T</i> conditions. Accordingly, the melt solidified into a monolithic BMG without nuclei in both Ti-rich and Cu-rich regions under small Δ<i>T</i> conditions. Moreover, a change in the phase stability of undercooled liquids could be expected with increasing Δ<i>T</i> by considering a non-classical model for the nucleation of glass-forming systems. The evolution of the liquid phase stability by modulating Δ<i>T</i> significantly influenced the crystallization behavior of the undercooled liquid. Understanding the microstructural evolution in the TiCu-based BMGs with changes in Δ<i>T</i> will assist in comprehending nanoscale chemical heterogeneities and the stability of the undercooled liquid, which could contribute to the optimization of the glass-forming behavior of BMGs with liquid phase separation and to the control of crystalline phase in BMG composites.</p> Graphical abstract <p></p>