The Mumford-Shah (MS) model is an important technique for mesh segmentation. Many existing researches focus on piecewise constant MS mesh segmentation model with total variation regularization, which pursue the shortest length of boundaries. Different from previous efforts, in this article, we propose a novel piecewise smooth MS mesh segmentation model by utilizing the relaxed total generalized variation regularization (rTGV). The new model assumes that the feature function of a mesh can be approximated by the sum of piecewise constant function and asmooth function, and the rTGV regularization is able to characterize the high order discontinuity of the geometric structure. The newly introduced method is effective in segmenting meshes with irregular structures and getting the better boundaries rather than the shortest boundaries. We solve the new model by alternating minimization and alternating direction method of multipliers (ADMM). Our algorithm is discussed from several aspects, and comparisons with several state-of-art methods. Experimental results show that our method can yield competitive results when compared to other approaches. In addition, our results compare favorably to those of the several state-of-art techniques when evaluated on the Princeton Segmentation Benchmark. Furthermore, the quantitative errors and computational costs confirm the robustness and efficiency of the proposed method.