The precise and automatic cutting of sheep carcasses can improve the quality of mutton. Robots are widely used in meat processing because of their good repeatability and high precision. Two essential problems encountered in robot working of sheep carcass processing are robot calibration and cutting trajectory planning. A method of cutting sheep carcasses based on 3D point clouds with a dual-robot system was proposed in this study. The dual-robot system consists of a 3D scanning system, a fixing device for sheep carcasses, and a cutting robot. The calibration of the dual-robot system was completed by solving the matrix problem AXB=YCZ using the iterative method and the closed-form method. The 3D model of a sheep carcass was constructed using a 3D scanner. The cutting scheme of the cutting robot was planned based on the processed 3D point clouds. To show the feasibility of the proposed sheep carcass processing scheme, practical experiments were carried out. The results of the experiments show that the cutting robot can accurately perform the cutting actions according to the planned cutting scheme. The system proposed in this study can improve the efficiency and precision of sheep carcass cutting.