This study addresses well-posedness of a Mindlin-Timoshenko (MT) plate model that incorporates nonlinear viscous damping and nonlinear source term in Neumann boundary conditions. The main results verify local and global existence of solutions as well as their continuous dependence on the initial data in appropriate function spaces. Along with (Pei et al. in J Math Anal Appl 418(2):535-568, 2014, in Nonlinear Anal 105:62-85, 2014) this work completes the fundamental well-posedness theory for MT plates under the interplay of damping and source terms acting either in the interior or on the boundary of the plate.