The nonlinear interaction between the beta-induced Alfvén eigenmode (BAE) and the tearing mode (TM) observed in the HL-2A experiment is systematically studied with the hybrid kinetic-magnetohydrodynamic code M3D-K. It is found that the nonlinear growth of TM can lead to a gradient buildup on the magnetic island (MI) edge, and then triggers the destabilization of the linearly-stable BAE. Then, the triggered BAE together with TM can produce a significant redistribution of energetic particles. For BAE linearly-dominant-unstable case, the TM activity results in the inward motion of BAE mode structure, and the BAE can have a delay effect on the MI saturation. Furthermore, a high-frequency axisymmetric 'breathing' mode is generated by the mode coupling of BAE and TM, agreeing well with the experimental observation, and causes the synchronized periodic oscillation of MI width.