The present paper proposed a newly designed dexterous mobile parallel mechanism for fusion reactor vacuum vessel assembly, the robot system has advantages in terms of compact design, the capability to carry out heavy-duty machining tasks, is easy to evacuate, and has less space occupation than other robot systems in existence. Despite different robot systems having been studied in the fusion reactor, there is still a lack of research on mechanism development for vacuum vessel assembly, which is attractive to future fusion reactors. In the fusion reactor, the robot systems will carry out different tasks, such as welding and machining. The assembly tasks of the vacuum vessel will be performed from inside of the vacuum vessel on-site. Then the paper introduced the single-objective and multi-objective optimization design of the proposed mechanism, the optimized objective was considered to be a combination of parallel mechanism dynamic machining force, dexterity, stiffness and workspace volume. The design variables were derived from the geometry of the fixed and movable platforms, which include mass, inertia, the sizes of the platforms, and distances between universal joints located on the platforms. In the multi-objective optimization, non-dominated sorting genetic algorithm II was adopted and different trajectories were designed to simulate the machining process, which further turns the local optimization problem into a global optimization problem. Finally, the optimized results were extracted and analyzed. Simulation results indicated the effectiveness of the proposed multi-objective optimization approaches and multi-objective optimization was found to be more reliable than single-objective optimization.