Real-world microscopy data have a large amount of noise due to the limited light/electron that can be used to capture images. The noise of microscopy data is composed of signal-dependent shot noise and signal-independent read noise, and the Poisson-Gaussian noise model is usually used to describe the noise distribution. Meanwhile, the noise is spatially correlated because of the data acquisition process. Due to the lack of clean ground truth, unsupervised and self-supervised denoising algorithms in computer vision shed new light on tackling such tasks by utilizing paired noisy images or one single noisy image. However, they usually make the assumption that the noise is signal-independent or pixel-wise independent, which contradicts with the actual case. Hence, we propose M-Denoiser for denoising real-world microscopy data in an unsupervised manner. Firstly, the shatter module is used to break the dependency and correlation before denoising. Secondly, a novelly designed unsupervised training loss based on a pair of noisy images is proposed for real-world microscopy data. For evaluation, we train our model on optical and electron microscopy datasets. The experimental results show that M-Denoiser achieves the best performance both quantitatively and qualitatively compared with all the baselines.