Typical low-temperature frustrated triangular antiferromagnet CuFeO₂ is attracting extensive interest due to its narrow-band-gap semiconductor properties. High-quality and impurity-free CuFeO₂ epitaxial thin films would be preferable for fundamental studies on the physical and chemical properties. However, the heteroepitaxial growth of impurity-free CuFeO₂ thin films has been a significant challenge due to its narrow formation window in the Cu-Fe-O system as well as the metastable nature of the Cu¹⁺ cations. This work reports for the first time the fabrication and characterization of high-quality and impurity-free (00.1)-oriented CuFeO₂ epitaxial thin films grown with relaxed interfaces on (00.1) sapphire substrates by pulsed laser deposition. Below the critical thickness of around 16 nm, the films exhibit a rhombohedral structure with relatively good crystalline quality where all Cu ions appear to be in the 1+ oxidation state, while the rocking curves display a narrow full width at half maximum of about 0.11°. Increasing the thickness, the (111)-oriented γ-Fe₂O₃ nanograins grow embedded in the CuFeO₂ films. Here, an excess Fe³⁺-assisted growth mechanism is proposed to explain the iron oxide grain formation. This study provides insight into the heteroepitaxial growth of relaxed CuFeO₂ thin films with high purity and crystalline quality as an ideal sample design to characterize the fundamental properties of this material in view of potential device applications.