Globally, the largest earthquakes occur on subduction zones, and their associated tsunamis are one of the greatest potential hazards faced by nearby coastal communities. Such great (Mw>8) and giant (Mw>9) earthquakes cause subsequent post-seismic deformation in the wide area depending on viscous structures of crustal and mantle rocks and the frictional properties of the plate interface. In particular, progress of afterslip occurring at the down-dip of the main rupture region where coseismic stress changes are large significantly affects the post-seismic uplift of the cosesimically subsided coastal regions. However, for giant megathrust events, viscoelastic flow and deep afterslip are mechanically coupled to each other, relaxing stress changes induced by both coseismic and post-seismic slip. Here, we show the role of afterslip and viscoelastic relaxation, and their interplay in the aftermath of the 2011 Mw 9.0 Tohoku earthquake. We conduct a two-dimensional analysis of the post-seismic deformation with coeval slip on the subduction interface governed by rate-strengthening friction and distributed deformation away from the fault governed by a power-law rheology with transient creep. The power-law rheology with stress-driven afterslip well explains the observed post-seismic deformation field and its time series in the period 2011 to 2016. Moreover, the geodetic data indicate a persistent deep afterslip directly down-dip of the main rupture region that greatly affects the ongoing post-seismic coastal uplift. Mechanical coupling between viscoelastic relaxation and afterslip notably modifies both the afterslip distribution and the surface deformation. Thus, we find that it is important to consider the interplay of these two deformation mechanisms to more fully understand the geodynamics of the Japan trench during the early stage of the seismic cycle. Finally, we also point out that such mechanical coupling are critical to estimate the future recovery of the coseismically subsided coastal area.