Parsing the competition between buoyancy and flow motions in stably stratified shear layers is an essential step to disentangling the challenging problem of turbulent mixing in the ocean. In this study, we outline a framework for evaluating the role of structures in the mixing and apply it using experimental datasets obtained in a stratified inclined duct (SID). First, we follow the vorticity decomposition on the SID datasets in Jiang, Lefauve, Dalziel & Linden (2022) (J. Fluid Mech, vol. 947, A30) and statistically analyse the localised buoyancy-shear and buoyancy-vortex competitions. We then build an orthogonal framework consisting of vectors of shear and rotation. The alignment probability between the density gradient and the vectors at both Holmboe and turbulence regimes is systematically analysed. By projecting the density gradient onto the axes of the framework, we identify the role of different flow motions in the mixing of the scalar field. Finally, the relationship between the ratio and the irreversible mixing coefficient in the turbulent regime is studied. The method in this work provides an effective route to examine the contribution of different structures to overall mixing efficiency and further understanding of stratified turbulence mixing.