Stress is a physiological and psychological response to potentially threatening events. With the rapid development of the era, individuals have to face fast-growing stress. Not only the severe stress could lead individuals into anxiety and depression, but also contribute to physical diseases. Mindfulness relieves stress by focusing on the present and an attitude towards acceptance. However, previous researches on the effects of mindfulness on stress were inconsistent, ignoring the complexity and diversity of the processes, and lacked the in-depth investigation of the corresponding mechanisms as well. Monitoring and Acceptance Theory (MAT) provides a clearer mechanism of mindfulness by deconstructing the components of monitoring and acceptance. Therefore, this study is based on MAT to assess the effects of mindfulness on stress and its psychoneurological mechanisms. First, this review introduces the basic concepts and framework of MAT to clarify the conceptual content and psychological operation of monitoring and acceptance. Second, through analyzing the monitoring and acceptance, the inconsistency of the effect of mindfulness on stress is mainly related to the monitoring component. Then, reviewing the past research, this review reveals the neural mechanisms of monitoring and acceptance affecting stress from the cognitive and emotional perspectives. Furthermore, this review summarizes that mindfulness monitoring improves attention and control of stressful stimuli by enhancing attentional monitoring and executive control. While, acceptance relieves stress primarily by changing cognition appraisal and reducing emotional reactivity. In summary, this review expands and complements MAT, which will contribute to the theory and practice study in this field both nationally and internationally. In addition, this review explores the neural mechanisms of monitoring and acceptance affecting stress from the perspective of brain plasticity, summarizes and proposes some directions for further study. Future research should focus on the effects and mechanisms of monitoring; more attention should be paid to the importance of stress stimulus and stress appraisal; new experimental paradigms should be designed to directly assess the psychological and neural mechanisms of the effects of mindfulness on stress through MAT; mindfulness stress-relieving interventions should be improved in order to promote the alleviation of stress problems in contemporary society in practice.