Wave energy has received significant attention in both academic and industrial areas during the past few decades. Among all of Wave Energy Devices (WEC) devices, many researchers focus on modeling the point absorber since it can provide a large amount of power in a small simple device when compared with other technologies. In this present work, we developed an efficient Structured Adaptive Mesh Refinement (SAMR) framework to model the interactions between the wave and pointer absorber by directly solving the Naiver-Stokes equation in a conservative manner. In particular, the level set function is used to capture the air-water interface, and re-initialization across different levels is applied. The Discrete Immersed Boundary Method (DIBM) is applied to describe geometry of the pointer absorber and include its effects on the incoming wave, which is generated in the inlet and absorbed by using a sponger layer closed to the outlet. To save computational cost, meshes are only refined near the air-water interface and surface of point absorber. Specially, both non-subcycling, where a uniform time step is employed for all variables on composite levels, and subcycling, in which variables on different levels advance via different time steps, are embedded in the SAMR framework. Cases about wave generation and fluid-structure interaction are obtained to validate the above proposed algorithm. Results show that subcycling takes significantly less CPU hours than non-subcycling to model the wave and pointer absorber interaction. Heave motions under different wave inputs are compared with previous experiments as well as results from potential flow theory, which shows viscous effects are important in this process. Future work including coupling AMR with Turbulent Models (e.g. RANS or LES) are also listed as an extension.