Mobile manipulators that combine mobility and manipulability, are increasingly being used for various unstructured application scenarios in the field, e.g. vineyards. Therefore, the coordinated motion of the mobile base and manipulator is an essential feature of the overall performance. In this paper, we explore a whole-body motion controller of a robot which is composed of a 2-DoFs non-holonomic wheeled mobile base with a 7-DoFs manipulator (non-holonomic wheeled mobile manipulator, NWMM) This robotic platform is designed to efficiently undertake complex grapevine pruning tasks. In the control framework, a task priority coordinated motion of the NWMM is guaranteed. Lower-priority tasks are projected into the null space of the top-priority tasks so that higher-priority tasks are completed without interruption from lower-priority tasks. The proposed controller was evaluated in a grapevine spur pruning experiment scenario.