Despite being two important problems in audio signal processing that are interconnected in practice, audio inpainting and audio source separation have not been considered jointly. It is not uncommon in practice to have the mixtures to be separated which also suffer from artifacts due to clipping or other losses. In present work, we consider this problem of source separation using partially observed mixtures. We introduce a flexible framework based on non-negative tensor factorisation (NTF) to attack this new task, and we apply it to source separation with clipped mixtures. It allows us to perform declipping and source separation either in turn or jointly. We investigate experimentally these two regimes and report large performance gains compared to source separation with clipping artefacts being ignored, which is the common approach in practice.