The cognitive processes supporting complex animal behavior are closely associated with ubiquitous movements responsible for our posture, facial expressions, ability to actively sample our sensory environments, and other critical processes. These movements are strongly related to neural activity across much of the brain and are often highly correlated with ongoing cognitive processes, making it challenging to dissociate the neural dynamics that support cognitive processes from those supporting related movements. In such cases, a critical issue is whether cognitive processes are separable from related movements, or if they are driven by common neural mechanisms. Here, we demonstrate how the separability of cognitive and motor processes can be assessed, and, when separable, how the neural dynamics associated with each component can be isolated. We establish a novel two-context behavioral task in mice that involves multiple cognitive processes and show that commonly observed dynamics taken to support cognitive processes are strongly contaminated by movements. When cognitive and motor components are isolated using a novel approach for subspace decomposition, we find that they exhibit distinct dynamical trajectories. Further, properly accounting for movement revealed that largely separate populations of cells encode cognitive and motor variables, in contrast to the 'mixed selectivity' often reported. Accurately isolating the dynamics associated with particular cognitive and motor processes will be essential for developing conceptual and computational models of neural circuit function and evaluating the function of the cell types of which neural circuits are composed.