Constrained multi-objective optimization problems (CMOPs) contain the satisfaction of various constraints and optimization of multiple objectives simultaneously, thus they are extremely challenging. Although many constrained multi-objective evolutionary algorithms (CMOEAs) have been proposed, they ignore the information of each constraint, which might help utilize more various infeasible solutions to improve the search ability of the population. Therefore, this paper proposes a new dual-population CMOEA to solve CMOPs, in which a dynamic constraint processing mechanism and a dynamic resource allocating scheme are designed. To be specific, the proposed algorithm evolves two populations, which adopt different mechanisms to handle constraints respectively. The main population directly optimizes all constraints to find the feasible Pareto optimal solutions, which can improve the feasibility. The auxiliary population adopts a dynamic constraint processing mechanism, which gradually increases the number of constraints being processed, so as to fully utilize various infeasible solutions to help find feasible regions. Moreover, a new dynamic resource allocating scheme is proposed to reasonably allocate the limited computational resources to the two populations according to their performance feedback. Experimental results on three test suites and ten practical problems show that the proposed algorithm has a better or competitive performance compared with several state-of-the-art CMOEAs.