The right of education and discipline is an important way of school education and teaching management, teachers to fulfill the teaching and educating people, the implementation of the fundamental task of moral education. This paper firstly discusses the dilemma of exercising the right to discipline teachers in education, and also analyzes the legal nature of the right to discipline in education and the impact on the emotional performance of teachers and students in the process of exercising the right. Secondly, cochlear filtering combined with CNN and LSTM network is introduced to extract the speech characteristics of teachers in the process of exercising the right of education and discipline, and a hybrid neural network model is used to realize the recognition and prediction of students’ auditory emotions. Finally, in order to verify the effectiveness of the method of this paper, experimental test analysis was carried out, and a comprehensive rule of law guarantee proposal was given in the process of exercising the right of teachers’ educational discipline. The results show that the maximum value of the intensity of the teacher’s speech signal after processing using the cochlear filter is 78.28dB, and the difference with the original signal is only 0.32%. The accuracy of recognizing students’ auditory emotions reached 90.48% after over 50 iterations. Under the background of big data, the right to discipline teachers in education needs to be analyzed with the help of technology for the data analysis of the appropriateness of exercise, and it is united in a number of aspects, such as strengthening the legislation, standardizing the implementation, strengthening the supervision, and perfecting the relief, as a way to help the comprehensive rule of law operation of the right to discipline teachers in education.