HOGMep is a novel Bayesian method for joint restoration and clustering on generic multi-component graph data. First, it uses a finite mixture of Multivariate Exponential Power (MEP) distributions as a prior model for graph signals. The general MEP form is capable of modeling broad types of signals including Gaussian, Laplacian or sparser ones. Second, a general Higher-Order Graphical Model (HOGM) on labels, encompassing the widely-used Potts model, is used to incorporate spatial relationships between neighboring graph signals. The generality of our model can tackle a large variety of data structures. Third, in contrast with regularized minimization approaches often adopted in the literature, our algorithm reliably estimates regularization parameters from observations. Such modeling leads to a complex posterior distribution of unknown parameters. This problem is tackled by Variational Bayesian Approximation (VBA) whose goal is to provide accurate approximation of the posterior distribution allowing us to efficiently compute posterior mean estimates. We demonstrate the effectiveness of HOGMep on the joint deconvolution and segmentation of color images interpreted as graph signals. Experiments show that the proposed approach outperforms state-of-the-art methods in both restoration performance and segmentation accuracy.