This paper addresses the problem of adaptive blind sparse source separation in the time domain of an over-determined instantaneous noisy mixture. A two-step approach is proposed: first, the data are projected on the signal subspace estimated using the principal subspace tracker FAPI. In the second step, an L1 criterion is used to represent the sparsity property of the signal sources. For the optimization of this cost function, an adaptive method based on Givens and Shear rotations is used. This algorithm, referred to SGDS-FAPI, guarantees low computational complexity which is essential in the adaptive context. Numerical simulations have been performed, and showed that the proposed algorithm outperforms existing solutions in both convergence speed and estimation quality.