In order to resolve the problem of cutter rotation controlling in the process of cutting using in CNC cutting machine tool, the principle of cutting of CNC cutting machine-tool is analyzed and the coordinate of the machine tool’s motion is built. Tangent Following interpolation of arc based on data sampling algorithm is researched. Interpolation formula is educed and its arithmetic flow chart is given. Two kinds of inaccuracy are analyzed and their comparison graph is studied. PC and Controller motion control system is used in this paper and close-loop speed control system is selected. Dynamic simulation of this interpolation is realized by testing the program written by VC++6.0 under the Googol motion control platform. The result shows that the Tangent Following interpolation can satisfy the need of cutting control process well.