We report a nonlinear acoustic system displaying excitability. The considered system is a magnetostrictive material where acoustic waves are parametrically generated. For a set of parameters, the system presents homoclinic and heteroclinic dynamics, whose boundaries define an excitability domain. The excitable behavior is characterized by analyzing the response of the system to different external stimuli. Single-spiking and bursting regimes have been identified. All these neuronlike properties are here predicted to occur in magnetostrictive materials, which are the basis of many smart systems and applications.