Reconfigurable multifunctional electromagnetic absorbers have shown broad application prospects in effectively dealing with a series of problems caused by complex electromagnetic environments due to their dynamic reflection wave control characteristics. In this work, we experimentally propose a multifunctional absorber based on a graphene metasurface. Its absorption mode can be flexibly switched among three modes of dual band, broadband, and single band. The reflection amplitude in each absorption mode can be controlled simultaneously. The measurement results of the prepared graphene metasurface indicate that the absorption modes and amplitudes can be dynamically controlled by changing two independent sets of bias voltages applied to the patterned graphene sandwich structures. The proposed graphene metasurface achieves peak absorption rates above 99.9% in both dual-band and single-band absorption modes. Specifically, in the broadband absorption mode, the bandwidth with an absorption rate greater than 90% reaches 17.8 GHz. In addition, it also integrates many advantages, such as optical transparency, polarization-insensitivity, stability of oblique incidence angles, and conformability to the application targets. Therefore, the proposed graphene metasurface is expected to be applied in platforms with optical windows that require resistance to electromagnetic interference and avoidance of electromagnetic radiation.