Amorphous alumina (a-AlOx), which plays important roles in several technological fields, shows wide variation of the density and composition. However, their influences on the properties of a-AlOx have rarely been investigated from a theoretical perspective. In this study, high dimensional neural network (NN) potentials were constructed to generate a series of atomic structures of a-AlOx with different densities (2.6–3.3 g/cm3) and O/Al ratios (1.0–1.75). The structural, vibrational, mechanical, and thermal properties of the a-AlOx models were investigated, as well as the Li and Cu diffusion behaviour in the models. The results showed that the density and composition had different degrees of effects on the different properties. The structural and vibrational properties were strongly affected by the composition, whereas the mechanical properties were mainly determined by the density. The thermal conductivity was affected by both the density and composition of a-AlOx. However, the effects on the Li and Cu diffusion behaviour were relatively unclear.