Free abrasive diamond wire saw machining is often used to cut hard and brittle materials, especially for wafers in the semiconductor and optoelectronics industries. Wire saws, both free and fixed abrasive, have excellent flexibility, as compared to inner circular saws, outer saws, and ribbon saws, as they produce a narrower kerf, lower cutting forces, and less material waste. However, fixed abrasive wire saw machining is being considered more and more due to its potential for increased productivity and the fact that it is more environmentally friendly as it does not use special coolants that must be carefully disposed. The cutting forces generated during the wire saw process strongly affect the quality of the produced parts. However, the relationship between these forces and the process parameters has only been explored qualitatively. Based on analyzing the forces generated from the chip formation and friction of a single abrasive, this study derives an analytical cutting force model for the wire saw machining process. The analytical model explains qualitative observations seen in the literature describing the relationship between the cutting forces and the wafer feed rate, wire velocity, and contact length between the wire and wafer. Extensive experimental work is conducted to validate the analytical force model. Silicon carbide (SiC) monocrystal, which is employed extensively in the fields of microelectronics and optoelectronics and is known to be particularly challenging to process due to its extremely high hardness and brittleness, is used as the material in these experimental studies. The results show that the analytical force model can predict the cutting forces when wire saw machining SiC monocrystal wafers with average errors between the experimental and predicted normal and tangential forces of 9.98% and 12.1%, respectively.