Both tunable perfect absorber and multifunctional logic device can be accomplished by a novel graphene metamaterial in this paper. The metamaterial utilizes gold as a substrate, covering with a graphene flake and a graphene double-strip-array on dielectric layers. First, the perfect absorption above 99.99% in the terahertz range is achieved depends on the coupling between the two graphene layers. In addition, the tunability is based on the correlation between the conductivity and the Fermi level of graphene. As the Fermi level changes, the absorption peak of the absorber will shift, thus the tunable perfect absorber is accomplished. On this basis, the input Boolean values of the logic function are defined by the Fermi levels of graphene. The output Booleans are distinguished by monitoring the reflections and comparing them with the thresholds. Finally, the multifunctional logic device have been successfully implemented in the terahertz domain. At different frequencies, the logic gates of OR, XNOR and NAND can be realized concurrently. And the NOT logic gate can be obtained synchronously at multiple frequencies. Furthermore, the operational frequencies of the aforementioned four logic functions can be tuned by varying the other Fermi level of graphene. The maximum extinction ratios of OR, XNOR, NAND, and NOT are 13.02 dB, 26.3 dB, 12.06 dB, and 26.3 dB, respectively. This multifunctional metamaterial has potential applications in terahertz optical communication due to its straightforward structure and multiple functions.