Due to the mechanism of the data acquisition process, hyperspectral imagery (HSI) are usually contaminated by various noises, e.g., Gaussian noise, impulse noise, strips, and dead lines. In this article, a spectral Mspatial L0 gradient regularized low-rank tensor factorization (LRTFL0) method is proposed for hyperspectral denoising, in which the restored HSI is approximated by low-rank block term decomposition (BTD). BTD factorizes a tensor into the sum of a series of component tensors, each of which is represented by the outer product of a matrix and a vector. From subspace learning point of view, the vector and matrix can be considered as a spectral atom and its corresponding coding coefficients. In the proposed method, the correlations in both spectral and spatial domains are taken into account via the small size of atom set and low-rankness of coding matrices. In addition, HSIs also have the local structure of piecewise smoothness in both spectral and spatial domains. Motivated by the supreme virtues of L0 gradient regularization in image structure exploitation, we develop a spectral Mspatial L0 gradient regularization and embed it into BTD to explore the spectral Mspatial texture information. The proposed method can simultaneously remove various types of noises, and the experimental results on both synthetic data and real-world data show its superiority when compared with several state-of-the-art approaches.