Teacher turnover presents a significant challenge in education. Despite recognizing the importance of examining turnover intention to address this issue, exploring the interplay between multiple job demands and turnover intention is lacking within the framework of the job demands-resources theory. To fill this gap, the present study theoretically examined the relationship among personal resources (career adaptability), job burnout, turnover intention, and various job demands (teaching–research and work–family conflicts). Data were collected through an online survey of 875 Chinese university teachers, and the conceptual model was estimated using maximum likelihood estimation. The results revealed that work–family and teaching–research conflicts directly predict teachers’ turnover intentions and that job burnout mediates between multiple job demands and turnover intentions. Furthermore, career adaptability moderates the mediating role of burnout. These findings offer innovative ideas for mitigating and preventing faculty turnover intentions.