Ultrasound and magnetization studies of the frustrated spinel ZnCr ₂Se ₄ are performed as a function of temperature and magnetic field up to 14 T. In zero field, the sound velocity and attenuation reveal significant anomalies at the antiferromagnetic transition at T _N 21 K indicating strong spin-lattice coupling. External magnetic fields shift these anomalies to lower temperatures concomitantly with the reduction of the Néel temperature. At 2 K, the sound velocity as a function of magnetic field manifests three pronounced anomalies: a deep minimum at 5.4 T related to an inflection point of the magnetization followed by two plateaus with distinct stiffness at fields above 7 and 10 T. The first plateau is ascribed to a transformation from a tetragonal to a cubic phase, while the second one corresponds to a state with fully polarized magnetization. The evolution of magnetic and structural states is discussed within a H-T phase diagram and compared with related frustrated magnetic spinels with strong spin-lattice coupling.