Radar-based noncontact physiological signals monitoring is meaningful for daily health monitoring, post-disaster rescue, and public security. This paper focuses on the theoretical and experimental study of noncontact respiratory and cardiac motion signals separation by remote sensing using a four-dimensional (4D) imaging radar. To adaptively separate respiratory and cardiac motion patterns, we propose a variational mode separation (VMS) algorithm. VMS is established on optimizing a variational problem to separate different modes. It minimizes the energy overlap of the heartbeat and respiration signals as well as their harmonics with an equality constraint. Both simulation and real scene data results show that the proposed VMS algorithm is suitable for separating the weaker cardiac motion pattern from the strong respiratory motion pattern, restraining the influence of respiration harmonics on the heartbeat component. Furthermore, we have implemented continuous remote monitoring of respiratory rate (RR) and heart rate (HR) by employing the proposed method in a real scene. The results validate the consistency with the reference respiration belt and electrocardiogram (ECG). The root mean square errors (RMSEs) of RR and HR for the remote measurement are 0.13 breaths per minute (brpm) and 1.7 beats per minute (bpm), respectively.