Since diarization and source separation of meeting data are closely related tasks, we here propose an approach to perform the two objectives jointly. It builds upon the target-speaker voice activity detection (TS-VAD) diarization approach, which assumes that initial speaker embeddings are available. We replace the final combined speaker activity estimation network of TS-VAD with a network that produces speaker activity estimates at a time-frequency resolution. Those act as masks for source extraction, either via masking or via beamforming. The technique can be applied both for single-channel and multi-channel input and, in both cases, achieves a new state-of-the-art word error rate (WER) on the LibriCSS meeting data recognition task. We further compute speaker-aware and speaker-agnostic WERs to isolate the contribution of diarization errors to the overall WER performance.