Dialogue act recognition is the task of classifying conversational utterances based on their communicative intent or function. To address this problem, we propose a novel two-phase processing approach called Dual-Process Masking. This approach streamlines the task by masking less important tokens in the input, identified through retrospective analysis of their estimated contribution during training. It enhances interpretability by using the masks applied during classification learning. Dual-Process Masking significantly improves performance over strong baselines for dialogue act recognition on a collaborative problem-solving dataset and three public dialogue benchmarks.