While deep generative models have empowered music generation, it remains a challenging and under-explored problem to edit an existing musical piece at fine granularity. In this paper, we propose SDMuse, a unified Stochastic Differential Music editing and generation framework, which can not only compose a whole musical piece from scratch, but also modify existing musical pieces in many ways, such as combination, continuation, inpainting, and style transferring. The proposed SDMuse follows a two-stage pipeline to achieve music generation and editing on top of a hybrid representation including pianoroll and MIDI-event. In particular, SDMuse first generates/edits pianoroll by iteratively denoising through a stochastic differential equation (SDE) based on a diffusion model generative prior, and then refines the generated pianoroll and predicts MIDI-event tokens auto-regressively. We evaluate the generated music of our method on ailabs1k7 pop music dataset in terms of quality and controllability on various music editing and generation tasks. Experimental results demonstrate the effectiveness of our proposed stochastic differential music editing and generation process, as well as the hybrid representations.