The crystal structure of the binary compound Cu₂Te has not been well-determined after decades of study. The hexagonal Nowotny structure was proposed in 1946; however, recent calculations showed that a new monoclinic structure and a trigonal one have much lower energies. Using first-principles calculations, we show that all the reported structures of Cu₂Te are metastable with respect to the phase separation Cu₂Te → Cu_2−xTe + xCu; i.e., Cu vacancies (Cu deficiency) can form spontaneously in Cu₂Te. The formation of Cu vacancies causes a structural transition of Cu_2−xTe from the monoclinic (most stable when x = 0), to the trigonal (0.125 ≤ x ≤ 0.625), and then to the hexagonal Nowotny structure (0.75 ≤ x < 1). The X-ray diffraction (XRD) spectra of these structures are simulated, showing that the experimental XRD peaks of four different Cu_2−xTe samples can be attributed to the trigonal structure. Based on this, we predict that the synthesized Cu_2−xTe samples (the Weissite mineral) with 0.125 ≤ x ≤ 0.625 should crystallize mainly in the trigonal rather than in the previously recognized hexagonal Nowotny structure. The lattice constants and atomic coordinates of different structures are calculated, which can be used in the future refinement of the Cu_2−xTe XRD spectra. Our study shows that the Cu-deficiency-induced structural transition should be considered in the study and application of Cu_2−xTe compounds.