Scalable distributed join processing in a parallel environment requires a partitioning policy to transfer data while minimizing the size of migrated statement and the number of communicated messages. Online theta-joins over data streams are more computationally expensive and impose higher memory requirement in distributed data stream management systems (DDSMS) than standalone database management systems (DBMS). The complete bipartite graph-based model can support distributed stream joins, and has the characteristics of memory-efficiency, elasticity and scalability. This is because each relation is stored in its corresponding processing units without data replicas and the units are independent of each other. However, due to the instability of data stream rate and the imbalance of attribute value distribution, the online theta-joins over skewed data streams can lead to the load imbalance of cluster. In this case, the bipartite graph-based model is unable to allocate the query nodes dynamically, and requires to set parameters about the grouping manually. The more serious issue is that the effect of the full-history join is worse. In this paper, a framework for handling skewed stream join is presented for enhancing the adaptability of the join model and minimizing the system cost based on the varying workloads. The proposal includes a mixed key-based and tuple-based partitioning scheme to handle skewed data in each side of the bipartite graph-based model, a strategy for redistribution of query nodes in two sides of this model, and a migration algorithm about state consistency to support full-history joins and adaptive resource management. Experiments with synthetic data and real data show that the presented method can effectively handle skewed data streams and improve the throughput of DDSMS, and it also effective especially on reducing the operational cost in the cloud environment.