Control processes associated with working memory play a central role in human cognition, but their underlying dynamic brain circuit mechanisms are poorly understood. Here we use system identification, network science, stability analysis, and control theory to probe functional circuit dynamics during working memory task performance. Our results show that dynamic signaling between distributed brain areas encompassing the salience (SN), fronto-parietal (FPN), and default mode networks can distinguish between working memory load and predict performance. Network analysis of directed causal influences suggests the anterior insula node of the SN and dorsolateral prefrontal cortex node of the FPN are causal outflow and inflow hubs, respectively. Network controllability decreases with working memory load and SN nodes show the highest functional controllability. Our findings reveal dissociable roles of the SN and FPN in systems control and provide novel insights into dynamic circuit mechanisms by which cognitive control circuits operate asymmetrically during cognition.