The physical mechanism and signal characteristics of acoustic scattering are the vital basis for target recognition. But underwater target acoustic scattering components are aliasing in time-frequency (TF) domain, for which the target elastic acoustic scattering characteristics are difficult to detect. Additionally, the existing blind source separation methods are effective only on condition that the number of array elements is equal to or greater than the number of the source signals. To address these problems, a novel TF domain blind source extraction method of separating target acoustic scattering components is proposed in this paper. The method only uses the TF energy characteristic differences among the target acoustic scattering components, and special limitations on target echo structures are unnecessary. Image morphology filter is used to remove the cross-term interference from time-frequency distribution (TFD) of the received array signals. Then, the single source which shows maximum energy concentration at the corresponding auto-term TF points is extracted through three operations: i) selecting the single source auto-term TF points from the auto-term ones; ii) constructing the spatial TFD matrix according to the selected single source auto-term TF points; iii) obtaining the single source by decomposing the eigenvalue of their spatial TFD matrix. Finally, the extracted single signal is excluded by the tightening process from the received array signals, and each single signal is separated successively by repeating the above steps. In addition, a signal processing model which can describe the physical characteristics of the target echoes is established based on the separated signal components. Simulations illustrate that the image morphological filter can remove the cross-term interference and improve the TF resolution of the Wigner-Ville distribution. Anechoic pool experimental results show that the TF domain blind source extraction algorithm can well separate each target acoustic scattering component, it can also achieve a higher output signal-to-noise ratio. Furthermore, the separated elastic acoustic scattering components are in good agreement with the results computed by the surface wave generating theory, so the method can provide the robust and reliable feature for underwater target recognition.