The traditional method of seismic data acquisition involves shots being separately excited, which results in low construction efficiency. Construction efficiency is significantly improved by the multi-source seismic mixed acquisition technology through the simultaneous or delayed excitation of multiple shots. However, substantial mixed noise is introduced to the seismic data by this technology, and the demixing efficiency of traditional methods is relatively low. To address this issue, the combination of the curvelet-transform with the fast threshold iteration method was used, and an exponential threshold model was applied to develop a fast and high-precision method for separating multi-source seismic data based on sparse inversion. During the curvelet domain separation process, a soft threshold function and exponential threshold model were utilized, resulting in favorable separation results after iterations. Additionally, the method's noise resistance performance was investigated. Theoretical numerical simulations and the application of field data demonstrated that the proposed method exhibits faster convergence, retains more effective signals, achieves higher-precision separation, and shows good performance on noise resistance compared to traditional separation methods.