Objectives optimization and constraints satisfaction are two equally important goals to solve constrained many-objective optimization problems (CMaOPs). However, most existing studies for CMaOPs can be classified as feasibility-driven-constrained many-objective evolutionary algorithms (CMaOEAs), and they always give priority to satisfy constraints, while ignoring the maintenance of the population diversity for dealing with conflicting objectives. Consequently, the population may be pushed toward some locally feasible optimal or locally infeasible areas in the high-dimensional objective space. To alleviate this issue, this article presents a problem transformation technique, which transforms a CMaOP into a dynamic CMaOP (DCMaOP) for handling constraints and optimizing objectives simultaneously, to help the population cross the large and discrete infeasible regions. The well-known reference-point-based NSGA-III is tailored under the problem transformation model to solve CMaOPs, namely, DCNSGA-III. In this article, ε -feasible solutions play an important role in the proposed algorithm. To this end, in DCNSGA-III, a mating selection mechanism and an environmental selection operator are designed to generate and choose high-quality ε -feasible offspring solutions, respectively. The proposed algorithm is evaluated on a series of benchmark CMaOPs with three, five, eight, ten, and 15 objectives and compared against six state-of-the-art CMaOEAs. The experimental results indicate that the proposed algorithm is highly competitive for solving CMaOPs.