Radar-based cardiac sensing has emerged as a promising approach for continuous and contactless health monitoring. However, most existing methods remain confined to laboratory settings, relying on handcrafted preprocessing, device-specific calibration, or auxiliary physiological supervision. These dependencies restrict scalability and limit practical deployment in real-world healthcare environments. We present CardioSSL, an end-to-end self-supervised radar sensing system for cardiac diagnosis directly from beamformed mmWave radar signals. CardioSSL integrates a lightweight spatiotemporal radar encoder with a multi-scale augmentation framework that simulates variability at the sensor, signal, and structure levels. By exposing the model to these variations during training, the framework encourages robust cardiopulmonary representations without relying on explicit subject identity or diagnostic labels. Evaluated on a large-scale clinical dataset of 7,336 patient recordings, CardioSSL achieves an average F1-score of 82.96%, outperforming both supervised and existing self-supervised baselines. These results suggest that self-supervised learning on beamformed radar signals is a promising foundation for scalable, contactless, and privacy-preserving cardiac monitoring.