Hyperspectral images (HSIs) are often severely degraded by mixed noise, such as Gaussian, stripe, and impulse noise during acquisition and transmission, which seriously impedes their subsequent applications. Therefore, HSI denoising is both crucial and challenging. In this work, we present a gradient-domain outlier-guided texture-preserved total variation (OG-TPTV) regularizer designed to remove mixed noise in HSIs. First, we utilize the mode-3 low-rank property of HSI gradient maps along the spectral dimension and apply a low-rank decomposition model to extract their spatial representation coefficients (SRCs). To improve the sparsity characterization of SRCs in the gradient subspace, an outlier-guided strategy is introduced. Specifically, we perform outlier detection on gradient maps to distinguish noise from texture structures and remove outliers to generate precise texture weighting maps. The resulting texture weight maps offer adaptive guidance for adjusting the strength of the sparsity constraints. Finally, a denoising method for HSIs is developed based on OG-TPTV. Extensive experiments on both synthetic and real HSIs demonstrate the superior denoising performance of our method.