Monocrystalline silicon is widely used in the semiconductor market, but its hard and brittle physical properties make processing difficult. Fixed-diamond abrasive wire-saw (FAW) cutting is currently the most commonly used cutting method for hard and brittle materials due to advantages such as narrow cutting seams, low pollution, low cutting force and simple cutting process. During the process of cutting a wafer, the contact between the part and the wire is curved, and the arc length changes during the cutting process. This paper establishes a model of contact arc length by analyzing the cutting system. At the same time, a model of the random distribution of abrasive particles is established to solve the cutting force during the cutting process, using iterative algorithms to calculate cutting forces and chip surface saw marks. The error between the experiment and simulation of the average cutting force in the stable stage is less than 6%, and the errors with respect to the central angle and curvature of the saw arc on the wafer surface are less than 5% between the experiment and simulation. The relationship between the bow angle, contact arc length and cutting parameters is studied using simulations. The results show that the variation trend of the bow angle and contact arc length is consistent, increasing with an increase in the part feed rate and decreasing with an increase in the wire velocity.