This paper presents a systematic approach for designing an ultra-wideband (UWB) absorber for terahertz (THz) applications. The metasurface consists of top patterned graphene (Gpat) and bottom continuous graphene (Gcont), each having a thickness of 0.335 nm and separated by a 3 μm thick silicon dioxide (SiO2) dielectric. Multiple absorbing modes have been generated by engraving rectangular, star-shaped, and circular ring slots on the top Gpat resonating at 3.22, 4.52, and 0.32 THz, respectively. A circular ring slot works as a coupling controller and helps to combine different slot resonances. The mode merger technique, along with the high plasmonic coupling between Gpat and Gcont controlled by Gcont help to attain an absorption bandwidth (BW) of 5.9 THz (193.44%) with absorptivity ≥ 90% ranging from 0.1 to 6 THz. The periodicity and thickness of the proposed polarization-insensitive metasurface are found to be λ0/300 and λ0/996.68, respectively, where λ0 is free space wavelength computed at 0.1 THz. Absorptivity ≥ 80% for incidence angle up to 60∘ under both transverse electric (TE) and transverse magnetic (TM) polarization has also been achieved. The absorber provides excellent frequency tunable characteristics over a UWB band and shows blue-shift with increased chemical potential (μc).