While cognitive diagnosis (CD) effectively assesses students' knowledge mastery from structured test data, applying it to real-world teacher-student dialogues presents two fundamental challenges. Traditional CD models lack a suitable framework for handling dynamic, unstructured dialogues, and it's difficult to accurately extract diagnostic semantics from lengthy dialogues. To overcome these hurdles, we propose DiaCDM, an innovative model. We've adapted the initiation-response-evaluation (IRE) framework from educational theory to design a diagnostic framework tailored for dialogue. We also developed a unique graph-based encoding method that integrates teacher questions with relevant knowledge components to capture key information more precisely. To our knowledge, this is the first exploration of cognitive diagnosis in a dialogue setting. Experiments on three real-world dialogue datasets confirm that DiaCDM not only significantly improves diagnostic accuracy but also enhances the results' interpretability, providing teachers with a powerful tool for assessing students' cognitive states. The code is available at https://github.com/Mind-Lab-ECNU/DiaCDM/tree/main.