Complex dexterous movements, such as reach-and-grasp, are driven by the coordinated activity of multiple brain regions. Each region contributes unique computations while interacting with others to control the movements. To understand the neural principles underlying this behavior across different brain regions, we recorded spiking activity in 10 brain regions while the mice performed a skilled reach-and-grasp task. We identified distinct behavioral phases, each with unique kinematic features. Single neuron analyses showed similar response percentages, with differing response strengths, across regions during different movement phases, though dynamical systems modeling of neural activity revealed distinct region-specific responses for each phase. Data-driven, multi-regional recurrent neural network (RNN) modeling combined with in silico electrophysiological perturbation experiments indicated a specialized role for secondary motor cortex (M2) influencing the activity of primary motor cortex (M1) only during a particular phase of the movement, while other regions had modest effects. Finally, simultaneous optogenetic inhibition of M2 and neural recordings in M1 confirmed these findings, with differential behavioral effects. Overall, we show that kinematically different movement components underlie the reach-and-grasp behavior. While the single unit responses occasionally were similar between different regions (although with some exceptions), the underlying dynamical rules (aka computations) are region-specific. These findings provide valuable insight into the specialized roles and interactions of different brain regions in controlling complex motor actions.