String theory predicts axions with a wide mass range and the Universe filled with such axions are called string axiverse. When the Hubble parameter roughly becomes comparable to the mass of an axion, the axion starts to oscillate. I first show that the axion can undergo a prominent resonance instability just after the onset of the oscillation. We studied non-linear dynamics of axions caused by the resonance instability based on semi-analytic computation and lattice simulation. We show that string axions with different masses generate gravitational waves (GWs) with peaks at various frequencies determined by the mass scales. This may allow us to explore string axiverse through future multi-frequency GW observations.