Wire saws with fixed diamond abrasive are often used to cut hard and brittle materials owning to the wire saw's narrow kerf, low cutting force, and minimal material waste. Typically, the cutting force changes during the operation since the part diameter and the contact length between the wire saw and part (i.e., contact length) continuously change, even if the process parameters (i.e., wire saw velocity, part feed rate, part rotation speed, and wire saw tension) are fixed, leading to wire saw breakage, wafer collapse, and inferior surface roughness. This study addresses this issue by regulating the force via feedback control. The most significant process parameter affecting the normal force, namely, part feed rate, is taken as the control variable. A system identification routine is used to obtain the transfer function relating the normal force and commanded part feed rate and the model parameters are identified online. An adaptive force controller is designed, and simulation and experimental studies for SiC monocrystal wafer wire saw machining are conducted. The results show the dynamic model well characterizes the normal force generated when wire saw machining SiC monocrystal, and the adaptive controller can effectively track various normal reference force trajectories (i.e., constants, ramps, and sine waves). The experimental results demonstrate that the wire saw machining process with adaptive force control can improve the cutting productivity and significantly decrease wafer surface roughness as compared to the cutting process with a constant part feed rate.