Acupoint therapy is a core therapeutic method of Traditional Chinese Medicine (TCM), and it requires a high level of expertise and skills to detect acupoints and perform acupuncture and moxibustion. Existing mixed reality (MR)-based training methods often fall short in accurate real-time detection and visualization of acupoints on the hand, limb, or torso of a real person and do not support various techniques of acupuncture and moxibustion. Moreover, evaluation standards and visual guidance with fine details for each step during MR-based training are typically missing. To this end, we propose the MR-based TCM Acupoint Therapy Teaching System (MRATTS)--an MR-based acupoint therapy teaching and training framework. MRATTS is based on a real-time hand, limb, and torso acupoint detection method to accurately track and visualize acupoints on real patients through MR. On top of that, in collaboration with an experienced acupoint therapist, we design a practice method with interactive visual guidance for various acupoint therapy techniques that simulate acupressure, acupuncture (insertion, lifting-thrusting, and twisting), and moxibustion (mild, sparrow-pecking, and whirling). A set of TCM theory-based evaluation standards is formulated within MRATTS to enable the scoring and visualization of the accuracy and proficiency of acupoint therapy. The effectiveness and usefulness of MRATTS are evaluated through a controlled user study and expert feedback. Results of the study indicate that the MRATTS group shows clear improvements in understanding 3D locations of acupoints and proficiency in acupoint therapy compared to control groups.