Remarkable properties of two-dimensional (2D) layer magnetic materials, which include spin filtering in magnetic tunnel junctions and the gate control of magnetic states, were demonstrated recently^{1,2,3,4,5,6,7,8,9,10,11,12}. Whereas these studies focused on static properties, dynamic magnetic properties, such as excitation and control of spin waves, remain elusive. Here we investigate spin-wave dynamics in antiferromagnetic CrI₃ bilayers using an ultrafast optical pump/magneto-optical Kerr probe technique. Monolayer WSe₂ with a strong excitonic resonance was introduced on CrI₃ to enhance the optical excitation of spin waves. We identified subterahertz magnetic resonances under an in-plane magnetic field, from which the anisotropy and interlayer exchange fields were determined. We further showed tuning of the antiferromagnetic resonances by tens of gigahertz through electrostatic gating. Our results shed light on magnetic excitations and spin dynamics in 2D magnetic materials, and demonstrate their potential for applications in ultrafast data storage and processing.