In hyperspectral images (HSIs), mixed noise (e.g., Gaussian noise, impulse noise, stripe noise, and deadlines) contamination is a common phenomenon that greatly reduces the visual quality of the image. In recent years, methods combining global and nonlocal low-rankness have been widely used in the field of HSI denoising. However, most methods apply original space-based denoising strategies (low-rank tensor decomposition, total variation, tensor sparse representation, and so on) directly to the modeling of nonlocal low-rank tensors in subspace, without fully exploiting the intrinsic and latent properties of the nonlocal similar tensors. In this article, we propose a hybrid prior denoising method based on global tensor low-rankness and nonlocal singular value decomposition (SVD)-aided group sparsity (GTL_NSGS). This method introduces a novel plug-and-play NSGS denoiser that uses SVD as assistance to successively explore self-similarity of spatial dimension, low-rankness of spectral dimension, and group sparsity of difference domain in subspace nonlocal similar tensors. Globally, we utilize the existing three-way log-based tensor nuclear norm (3DLogTNN) to approximate the HSI tensor fibered rank and introduce a difference continuity regularization to obtain a continuous smooth spectral basis. Finally, we combine the alternating direction method of multipliers (ADMM) with the augmented Lagrangian multiplication (ALM) algorithm to solve the proposed model effectively. Extensive experiments on simulated and real datasets demonstrate that the proposed method has superior performance in removing mixed noise compared to state-of-the-art denoisers.