Integrated sensing and communications (ISAC), as a key enabling technology for 6 G, significantly enhances the application potential of Wi-Fi devices in non-contact vital sign monitoring by deeply integrating communication and sensing capabilities. Accurate monitoring of respiratory and heartbeat rates is crucial for early disease warning and real-time health status monitoring. However, current ISAC-based vital sign detection methods often suffer from suboptimal separation of respiratory and heartbeat signals and limited robustness against interference in complex environments. To address these challenges, a vital sign signal separation and frequency detection algorithm based on successive variational mode decomposition (SVMD) is proposed. Firstly, beamforming feedback information (BFI) is collected via Wi-Fi devices and preprocessed to obtain the beamforming matrix (BFM) signal. Subsequently, the ratio between each pair of elements in the beamforming matrix is calculated, and effective vital sign signals are accurately extracted from complex multipath environments by combining dynamic feature subcarrier screening and multi-stage denoising techniques. Furthermore, SVMD is introduced to leverage its characteristics of sequential extraction and independence from presetting the number of modes K. An adaptive parameter optimization method based on the artificial lemming algorithm (ALA) is designed to determine the key balance parameter in SVMD, enabling high-precision separation of respiratory and heartbeat signals. Finally, respirator and heartbeat rates are estimated using Fast Fourier Transform and peak detection. Experimental results demonstrate that, across various typical application scenarios, including user heterogeneity, deep breathing, post-exercise state, and varying distances, the proposed method effectively mitigates the impact of multipath effects and environmental noise, maintains stable detection performance, and significantly improves the estimation accuracy of respiratory and heartbeat rates compared to existing methods. The proposed algorithm provides a reliable solution for non-contact vital sign detection based on ISAC.