The synchronization of geodesic acoustic modes (GAMs) and magnetic islands has been observed in the edge plasmas of the HL-2A tokamak using multiple Langmuir probe arrays [K. J. Zhao et al., Phys. Rev. Lett, 117, 145002 (2016)]. New mesoscale electric fluctuations (MSEFs), resulting from the synchronization were identified [K. J. Zhao et al., Nucl. Fusion 57, 076036 (2017)]. In this paper, the responses of the synchronization to sawtooth heat pulses are investigated. Before sawtooth crashes, the coherencies between islands and MSEFs are higher and their phase shifts almost do not vary. After sawtooth crashes, the MSEF drops significantly. The coherencies between islands and MSEFs decrease and their phase shifts change rapidly. This analysis suggests that the synchronization can be broken by sawteeth. However, when the coupling of the GAM and islands becomes strong, the synchronization still sustains during sawtooth crashes. In addition, the Lissajous curves of the MSEFs and turbulence intensity shows that the turbulence lags with the MSEFs.