Solving constrained multiobjective optimization problems (CMOPs) with various features and challenges via evolutionary algorithms is very popular. Existing methods usually adopt an additional helper problem to simplify and solve them by divide and conquer. This article proposes a new multitasking framework for CMOPs, borrowing the idea of evolutionary multitasking optimization. The main contributions are: 1) a multitasking framework is proposed, where a CMOP is modeled as a multitasking optimization problem with three tasks. Then, it is solved by constraint-first, constraint-ignored, and constraint-relaxed multiobjective evolutionary algorithms; 2) a knowledge expression and a transfer strategy are devised to transfer the knowledge among the tasks; and 3) based on the proposed framework, a new two-stage algorithm is presented to solve CMOPs. The effectiveness of our approach is validated through experiments on four CMOP benchmark suites and 19 real-world CMOPs.