Previous studies on cracked pipes have predominantly focused on single excitation, but in practical engineering, pipe systems often experience a combined effect of fluid pulsation and base excitations, which can potentially trigger more complex dynamic behaviors. Moreover, the solid finite element (FE) models are generally adopted to simulate the breathing effect and stress singularity, but the solution efficiency is unacceptable. Therefore, this study presents a spectral element-finite element (SE-FE) method to construct the dynamic models of the fluid-delivering cracked pipes (FDCPs), which combines the efficiency of spectral element (SE) with the adaptability of FE. Furthermore, a fluid pulsation model is constructed using measured data. Specifically, dynamic models of intact and cracked pipe segments are constructed using SE and FE, respectively, and interface coupling is achieved by the penalty function method. Subsequently, an experimental system for fluid pulsation excitation is established, and then a fluid pulsation model is constructed. Finally, the dynamic behaviors of a FDCP under compound excitation are analyzed. The results show that the fluid pulsation in the FDCP is higher than that in the intact pipe due to the breathing effect. Moreover, the beat vibration will be triggered when the pulsation frequency approaches the base excitation frequency. This study can provide a better understanding for the dynamic behaviors of FDCP, thereby providing a reference for crack damage detection.