In Nuclear Magnetic Resonance (NMR) spectroscopy, an efficient analysis and a relevant extraction of different molecule properties from a given chemical mixture are important tasks, especially when processing bidimensional NMR data. To that end, using a blind source separation approach based on a variational formulation seems to be a good strategy. However, the poor resolution of NMR spectra and their large dimension require a new and modern blind source separation method. In this work, we propose a new variational formulation for blind source separation (BSS) based on a $\beta$-divergence data fidelity term combined with sparsity promoting regularization functions. An application to 2D HSQC NMR experiments illustrates the interest and the effectiveness of the proposed method whether in simulated or real cases.