Acoustic data from the Industrial Internet of Things (IIoT) is widely used in anomaly detection because audio information reflects richer internal statuses of monitored working machines than the video does. Since multiple acoustic data sources interfere with each other by nature, source data estimation is a prerequisite of subsequent anomaly detection. Existing schemes often use a centralized manner to separate full data on a remote node in clouds. However, such a centralized manner may delay reactions to anomalies due to data transmission delay and the complexity of solving data separation problems. This paper shows that the data separation phase can be substantially accelerated with an in-network computing approach. The key idea is to offload data processing jobs to intermediate network nodes along the forwarding path. We first propose a distributed algorithm so that the data separation jobs can be done in a progressive manner; likewise, we modify the forwarding layer in order to eliminate hop-by-hop data transmission delay that hurts the performance of using in-network computing. We further derive theoretical upper and lower bounds of the required number of intermediate nodes that achieve the maximum acceleration. We also implement our proposed solution in a full-stack network emulator. Based on an open and professional dataset, evaluation results justify the feasibility and advantages of our idea with nearly 32.18% acceleration on total processing time. This work exemplifies the convergence of IIoT, edge, and clouds.