Graph-cuts are widely used in computer vision. In order to speed up the optimization process and improve the scalability for large graphs, Strandmark and Kahl introduced a splitting method to split a graph into multiple subgraphs for parallel computation in both shared and distributed memory models. However, this parallel algorithm (parallel BK-algorithm) does not have a polynomial bound on the number of iterations and is found non-convergent in some cases due to the possible multiple optimal solutions of its sub-problems. To remedy this non-convergence problem, in this work we first introduce a merging method capable of merging any number of those adjacent sub-graphs which could hardly reach an agreement on their overlapped region in the parallel BK algorithm. Based on the pseudo-boolean representations of graph cuts,our merging method is shown able to effectively reuse all the computed flows in these sub-graphs. Through both the splitting and merging, we further propose a dynamic parallel and distributed graph-cuts algorithm with guaranteed convergence to the globally optimal solutions within a predefined number of iterations. In essence, this work provides a general framework to allow more sophisticated splitting and merging strategies to be employed to further boost performance. Our dynamic parallel algorithm is validated with extensive experimental results.