Aimed at the problem that most existing many-objective evolutionary algorithms still cannot effectively balance convergence and diversity of the population in the high-dimensional space, this paper proposes an angle-decomposition assisted multi-stage evolutionary algorithm for many-objective optimization (AMEA). This algorithm collaborates the angle-decomposition mechanism and a multi-stage adaptive deletion strategy to eliminate individuals with poor performance one-by-one, and thus balance convergence and diversity of the population. Specifically, the former selects a pair of individuals with the minimum angle, which means they are the most similar; The latter adaptively eliminates individuals with poor performance based on the evolutionary state of the population. When the population does not converge to the Pareto front, this deletion strategy eliminates individuals with poor convergence to accelerate population convergence If these two individuals have the same convergence, the deletion strategy eliminates individuals with poor diversity. On the contrary, the deletion strategy utilizes the designed comprehensive performance indicators to eliminate individuals with poor convergence and diversity for improving the overall performance of the population. In addition, a mating selection strategy based on radial space projection is designed to select individuals with good convergence and diversity for variation, and further improves the ability of AMEA to explore the high-dimensional space. Experimental results show that AMEA has strong competitiveness in dealing with many-objective optimization problems compared with its competitors.