In non-contact heart rate (HR) monitoring via Doppler radar, the disturbance from respiration and/or body motion is treated as a key problem on the estimation of HR. This paper proposes a blind source separation (BSS) approach to mitigate the noise effect in the received radar signal, and incorporates the sparse spectrum reconstruction (SSR) to achieve a high-resolution of heartbeat spectrum. The proposed BSS decomposes the spectrogram of mixture signal into original sources including heartbeat using non-negative matrix factorization (NMF) algorithms, through learning the complete basis spectra (BS) by a hierarchical clustering. In particular, to exploit the temporal sparsity of heartbeat component, two variants of NMF algorithms with sparseness constraints are applied as well, namely sparse NMF (SPNMF) and weighted sparse NMF (WSPNMF). Compared with usual BSS, our proposed BSS has three advantages: (i) Clustering-induced unsupervised manner; (ii) Compact demixing architecture; and (iii) Merely requiring signal-channel input data. In addition, the HR estimation method using our proposal delivers more satisfactory precision and robustness over other existing methods, which is demonstrated through the measurements to distinguishing people's activities, gaining both smallest absolute errors of HR estimation for sitting still and typewriting.