The amorphous hafnia has a wide range of applications in microelectronic devices, and understanding its microscopic thermal transport mechanism is crucial for improving the performance and reliability of electronic devices. Most previous studies are based on molecular dynamics and the single quasi-harmonic Green-Kubo method, which makes it difficult to accurately consider the contribution of low-frequency vibrational modes to thermal conductivity. In this paper, based on the quasi-harmonic Green-Kubo method combined with hydrodynamic extrapolation, the heat transport mechanism of amorphous hafnia structures with different degrees of ordering is comprehensively investigated. The method effectively overcomes the finite size issue inherent in the single quasi-harmonic Green-Kubo method. Theoretical predictions show that the thermal conductivity of amorphous hafnia exhibits a weak correlation with the degree of microstructural ordering. Modal analysis reveals that low- and mid-frequency vibrational modes significantly contribute to thermal conductivity, which is the main reason for the underestimation of the thermal conductivity of amorphous hafnia in the single quasi-harmonic Green-Kubo method. Furthermore, this paper separates the contributions of propagons and diffusons to the thermal conductivity of amorphous hafnia using the anharmonic dynamic structure factor, revealing that diffusons dominate the thermal conductivity of all amorphous hafnia structures. However, the contribution of the propagons to thermal conductivity remains significant, reaching over 20% and increasing with the degree of ordering.