This research focuses on the realization of rapid reconfiguration in a cloud manufacturing environment to enable flexible resource scheduling, fulfill the resource potential and respond to various changes. Therefore, this paper first proposes a new cloud and software-defined networking (SDN)-based manufacturing model named software-defined cloud manufacturing (SDCM), which transfers the control logic from automation hard resources to the software. This shift is of significance because the software can function as the “brain” of the manufacturing system and can be easily changed or updated to support fast system reconfiguration, operation, and evolution. Subsequently, edge computing is introduced to complement the cloud with computation and storage capabilities near the end things. Another key issue is to manage the critical network congestion caused by the transmission of a large amount of Internet of Things (IoT) data with different quality of service (QoS) values such as latency. Based on the virtualization and flexible networking ability of the SDCM, we formalize the time-sensitive data traffic control problem of a set of complex manufacturing tasks, considering subtask allocation and data routing path selection. To solve this optimization problem, an approach integrating the genetic algorithm (GA), Dijkstra's shortest path algorithm, and a queuing algorithm is proposed. Results of experiments show that the proposed method can efficiently prevent network congestion and reduce the total communication latency in the SDCM.