In this article, the vector dynamics of semiconductor optical amplifiers (SOAs) are systematically analyzed and developed to explore its mechanism of intensity noise suppression. First, theoretical investigation on the gain saturation effect and carrier dynamics is performed via a vectorial model, and the calculated result unravels desynchronized intensity fluctuations of two orthogonal polarization states. Particularly, it predicts an out-of-phase case, which allows the cancellation of the fluctuations via adding up the orthogonally-polarized components, then establishes a synthetic optical field with stable amplitude and dynamic polarization, and thereby enables a remarkable relative intensity noise (RIN) reduction. Here, we term this approach of RIN suppression as out-of-phase polarization mixing (OPM). To validate the OPM mechanism, we conduct an SOA-mediated noise-suppression experiment based on a reliable single-frequency fiber laser (SFFL) with the presence of relaxation oscillation peak, and subsequently carry out a polarization resolvable measurement. By this means, out-of-phase intensity oscillations with respect to the orthogonal polarization states are clearly demonstrated, and consequently enable a maximum suppression amplitude of >75 dB. Notably, the RIN of 1550-nm SFFL, suppressed by joint action of OPM and gain saturation effect, is dramatically reduced to -160 dB/Hz in a wideband of 0.5 MHz∼10 GHz, and the performance of which is excellent by comparing with the corresponding shot noise limit of -161.9 dB/Hz. The proposal of OPM here not only facilitates us to dissect the vector dynamics of SOA but also offers a promising solution to realize wideband near-shot-noise-limited SFFL.