The γ-TiAl alloy is widely used in the aerospace industry due to its remarkable properties. However, its deformation mechanism during nanocutting is significantly influenced by temperature variations. This study utilizes molecular dynamics simulations to investigate the nanocutting processes of polycrystalline γ-TiAl alloy across a range of low and high temperatures. The focus is on how the initial equilibrium temperature affects cutting force, cutting temperature, Von Mises stress, shear strain, atomic phase transformation, and dislocation evolution during the nanocutting of the alloy.The results indicate that at lower temperatures, a decrease in initial equilibrium temperature leads to a gradual increase in the number of atoms in intermediate states, accompanied by diminished heat diffusion. Conversely, in high-temperature cutting scenarios, the initial equilibrium temperature is negatively correlated with the cutting force (Fx); specifically, the average Fx at 300K is 1.72 times that at 1050K. At elevated temperatures, as the initial equilibrium temperature increases, the chip formation mode transitions from fracture to shear, resulting in higher internal Von Mises stress and shear strain within the chips, as well as a wider shear line. Additionally, further increases in the initial equilibrium temperature lead to a broader atomic flow bandwidth in the shear region.At 173K, the counts of BCC and HCP structured atoms reach their minima, comprising 62.5 % and 55 % of their respective maximum values. Moreover, the densities of 1/2<110> (perfect) dislocations and 1/3<111> (Frank) dislocations decrease with rising initial equilibrium temperatures, showing growth rates exceeding 80 % as the temperature increases from 300K to 1050K.