We study the dynamical state and the integrated total mass profiles of 75 massive (M500 > 5 × 1014 M⊙) Sunyaev–Zeldovich(SZ)-selected clusters at 0.08 < z < 1.1. The sample is built from the Planck catalogue, with the addition of four SPT clusters at z > 0.9. Using XMM-Newton imaging observations, we characterise the dynamical state with the centroid shift ⟨w⟩, the concentration CSB, and their combination, M, which simultaneously probes the core and the large-scale gas morphology. Using spatially resolved spectroscopy and assuming hydrostatic equilibrium, we derive the total integrated mass profiles. The mass profile shape is quantified by the sparsity, that is the ratio of M500 to M2500, the masses at density contrasts of 500 and 2500, respectively. We study the correlations between the various parameters and their dependence on redshift. We confirm that SZ-selected samples, thought to most accurately reflect the underlying cluster population, are dominated by disturbed and non-cool core objects at all redshifts. There is no significant evolution or mass dependence of either the cool core fraction or the centroid shift parameter. The M parameter evolves slightly with z, having a correlation coefficient of ρ = −0.2 ± 0.1 and a null hypothesis p-value of 0.01. In the high-mass regime considered here, the sparsity evolves minimally with redshift, increasing by 10% between z < 0.2 and z > 0.55, an effect that is significant at less than 2σ. In contrast, the dependence of the sparsity on dynamical state is much stronger, increasing by a factor of ∼60% from the one third most relaxed to the one third most disturbed objects, an effect that is significant at more than 3σ. This is the first observational evidence that the shape of the integrated total mass profile in massive clusters is principally governed by the dynamical state and is only mildly dependent on redshift. We discuss the consequences for the comparison between observations and theoretical predictions.