It was recently shown that there exists a narrow parameter window where benign sawtooth crashes cause only mixing of bulk plasma and slowed-down alpha particle 'ash', while leaving MeV-class fast alphas largely unperturbed (Bierwage et al 2022 Nat. Commun.13 3941). Here, we revisit the underlying physical picture and reframe it in a manner that may be suitable for systematic analyses of this phenomenon in modeling, simulation and experimental studies. In particular, we propose a graph that we call 'time-helicity de-resonation diagram' (short: T-H diagram) that captures the physical essence of energy-selectivity of sawtooth-particle interactions and visualizes it in a compact, intuitive way. Moreover, the regimes of good confinement and strong mixing during a sawtooth crash can be discerned via a single figure of merit: the T-H radius. The concept is introduced here on the basis of simulation results and would eventually benefit from further validation when applied to suitable empirical data.