R2 indicator based multi-objective evolutionary algorithms (R2-MOEAs) have achieved promising performance on traditional multi-objective optimization problems (MOPs) with two and three objectives, but still cannot well handle many-objective optimization problems (MaOPs) with more than three objectives. To address this issue, this paper proposes a two-stage R2 indicator based evolutionary algorithm (TS-R2EA) for many-objective optimization. In the proposed TS-R2EA, we first adopt an R2 indicator based achievement scalarizing function for the primary selection. In addition, by taking advantage of the reference vector guided objective space partition approach in diversity management for many-objective optimization, the secondary selection strategy is further applied. Such a two-stage selection strategy is expected to achieve a balance between convergence and diversity. Extensive experiments are conducted on a variety of benchmark test problems, and the experimental results demonstrate that the proposed algorithm has competitive performance in comparison with several tailored algorithms for many-objective optimization.