We present a parallel version of the cut-pursuit algorithm for minimizing functionals involving the graph total variation. We show that the decomposition of the iterate into constant connected components, which is at the center of this method, allows for the seamless parallelization of the otherwise costly graph-cut based refinement stage. We demonstrate experimentally the efficiency of our method in a wide variety of settings, from simple denoising on huge graphs to more complex inverse problems with nondifferentiable penalties. We argue that our approach combines the efficiency of graph-cuts based optimizers with the versatility and ease of parallelization of traditional proximal