The field of applied wire electrical discharge machining (WEDM) is rapidly expanding due to rapidly increasing demand for parts made of hard-to-machine materials. Hard alloys composed of WC, TiC and Co are advanced cutting materials widely used in industry due to the excellent combination of hardness and toughness, providing them obvious advantages over other cutting materials, such as cubic boron nitride, ceramics, diamond or high-speed steel. A rational choice of the WEDM modes is extremely important to ensure the dimensional quality of the manufactured cutting inserts, while roughness of the machined surface on the cutting edge is of great importance with regards to the application of wear-resistant coatings, which increases tool life. However, the stock control systems of CNC WEDM machines, which are based on assessment of electrical parameters such as amperage and voltage, are unable to timely detect conditions at which a threat of wire breakage appears and to prevent wire breakage by stopping the electrode feed and flushing out the interelectrode gap (IEG) when hard alloys with high heat resistance and low heat conductivity, such as WC, TiC and Co composites, are being machined, due to the inability to distinguish the working pulses and pulses that expend a part of their energy heating and removing electroerosion products contaminating the working zone. In this paper, the physicomechanical nature of the WEDM of hard alloy WC 88% + TiC 6% + Co 6% was investigated, and the possibility of using acoustic emission parameters for controlling WEDM stability and productivity were explored. Acoustic emission (AE) signals were recorded in octave bands with central frequencies of 1–3 and 10–20 kHz. It was found that at the initial moment, when the dielectric fluid is virtually free of contaminants, the amplitude of the high-frequency component of the VA signal has its highest value. However, as the contamination of the working zone by electroerosion products increases, the amplitude of the high-frequency component of the AE signal decreases while the low-frequency component increases in an octave of 1–3 kHz. By the time of the wire breakage, the amplitude of the high-frequency component in the octave of 10–20 kHz had reduced by more than 5-fold, the amplitude of the low-frequency component in the octave of 1–3 kHz had increased by more than 2-fold, and their ratio, coefficient Kf, decreased by 12-fold. To evaluate the efficiency of Kf as a diagnostic parameter, the quality of the surface being machined was investigated. The analysis of residual irregularities on the surface at the electrode breakage point showed the presence of deep cracks and craters typical of short-circuit machining. It was also found that the workpiece surface was full of deposits/sticks, whose chemical composition was identical to that of the wire material. The presence of the deposits evidenced heating and melting of the wire due to the increased concentration of contaminants causing short circuits. It was also shown that the wire breakage was accompanied by the “neck” formation, which indicated simultaneous impacts of the local heating of the wire material and tensile forces. Due to the elevated temperature, the mechanical properties the wire material are quickly declining, a “neck” is being formed, and, finally, the wire breaks. At the wire breakage point, sticks/deposits of the workpiece material and electroerosion products were clearly visible, which evidenced a partial loss of the pulses’ energy on heating the electroerosion products and electrodes. A further increase in the contamination level led to short circuits and subsequent breakage of the wire electrode. It was shown that in contrast to the conventional controlling scheme, which is based on the assessment of amperage and voltage only, the analysis of VA signals clearly indicates the risk of wire breakage due to contamination of the working zone, discharge localization and subsequent short circuits. The monotonic dependence of WEDM productivity on AE parameters provides the possibility of adaptive adjustment of the wire electrode feed rate to the highest WEDM productivity at a given contamination level. As the concentration of contaminants increases, the feed rate of the wire electrode should decrease until the critical value of the diagnostic parameter Kf, at which the feed stops and the IEG flushes out, is reached. The link between the AE signals and physicomechanical nature of the WEDM of advanced cutting materials with high heat resistance and low heat conductivity in different cutting modes clearly shows that the monitoring of AE signals can be used as a main or supplementary component of control systems for CNC WEDM machines.