The energy landscape of ZrO2-doped amorphous Ta2O5 is explored in this work. With models corresponding to experimental concentrations of 50% Zr and 50% Ta cations, we search for, gather, and analyze two-level systems (TLSs) from molecular dynamic simulations. The mechanical loss function is calculated for each TLS individually. The results show that TLS with low asymmetry and large elastic coupling constants contribute the most to mechanical loss. We identify these as "bad actors." The higher barriers relate to the mechanical loss at higher temperatures. The concept of the oxygen cage that describes the local structural environment surrounding a metal ion is introduced. The existence of a drastic change in local environment, or a cage-breaking process, enables us to understand the double peaks present in the asymmetry distribution and provides a pictorial interpretation to distinguish two types of TLS. Quantitatively, a cage-breaking event is related to at least one large distance change in an atom-atom pair, and non-cage-breaking transitions have only small rearrangements. The majority of TLSs are cage-breaking transitions, but non-cage-breaking TLS transitions show higher average mechanical loss in ZrO2-doped Ta2O5. By decomposing the contributions to mechanical loss, we find that the low temperature loss peak near 40 K mainly comes from non-cage-breaking TLS transitions and the second loss peak near 120 K originates from cage-breaking TLS transitions. This finding is important for understanding the interplay between the atomic structure of TLS and mechanical loss.