Diamond wire sawing is the main processing method for hard and brittle materials, but the unreasonable matching of process parameters will reduce its cutting ability and stability. In this paper, the asymmetric arc hypothesis of a wire bow model is proposed. Based on this hypothesis, an analytical model of the wire bow between the process parameters and the wire bow parameters was established and verified with a single-wire cutting experiment. The model considers the asymmetry of the wire bow in diamond wire sawing. The tension at both ends of the wire bow is called the endpoint tension; by calculating the difference in tension between the two ends, a reference for the cutting stability and a tension range for the selection of the diamond wire were provided. The model was used to calculate the wire bow deflection and the cutting force, providing theoretical guidance for the matching of process parameters. Based on the theoretical analysis of the cutting force, endpoint tension and wire bow deflection, the cutting ability, cutting stability, and the risk of wire cutting were predicted.