This article uses a control volume method to analyze the circumferential groove casing treatment in a transonic compressor. To analyze the axial momentum transport through the tip gap, the control volume near the casing is divided into two parts: the control volumes inside and outside the tip gap. Besides, the association between the forces acting on the control volume and flow structures is studied by analyzing the distributions of axial momentum flux and axial shear stress. With this method, the flow mechanisms of stall margin improvement due to casing grooves in Rotor 35 are quantitatively analyzed. The analysis is conducted at 100% and 60% design speed with supersonic and subsonic tip speed, respectively. At design speed, the casing grooves decrease the axial shear force and the axial force due to the transport of axial momentum induced by the tip leakage flow. Meanwhile, the bleeding and injecting effect of grooves contribute much to the axial force due to the transport of axial momentum. Based on the axial distribution of the axial forces, the contribution of each groove to the stall margin improvement is assessed. And the grooves that play a major role in stall margin improvement are ascertained. At 60% design speed, because the blade loading is reduced, the axial momentum transport caused by the grooves cannot suppress the boundary layer separation effectively. Consequently, the stall margin of the compressor is not significantly improved by the casing grooves.