Acoustic feature extraction of radiation pressure signals (RPSs) induced by bubble oscillations is a crucial task in the characterization of the properties of underwater objects. In this article, to improve the extraction accuracy, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and bubble entropy (BE) algorithms are combined to extract the effective acoustic components of the RPS. For verification, the proposed extraction scheme is applied to a typical simulated RPS under dual-frequency acoustic excitation. Compared with other extraction methods, CEEMDAN can extract richer acoustic feature information from the RPS, including accurate values for the amplitude and period of oscillation. Furthermore, when the components of the simulated RPS become more complex, the CEEMDAN–BE scheme gives better evaluation results than other schemes in terms of three evaluation indices. Under complex conditions, the signal extraction performances of singular value decomposition and ensemble empirical mode decomposition decrease greatly, but CEEMDAN retains its high signal extraction efficiency, which further confirms the effectiveness of the proposed signal extraction scheme.