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This paper describes the design of a bionic soft exoskeleton and demonstrates its feasibility for assisting the expectoration function rehabilitation of patients with spinal cord injury (SCI). <italic>Methods:</italic> A human&#x2013;robot coupling respiratory mechanic model is established to mimic human cough, and a synergic inspire&#x2013;expire assistance strategy is proposed to maximize the peak expiratory flow (PEF), the key metric for promoting cough intensity. The negative pressure module of the exoskeleton is a soft &#x201C;iron lung&#x201D; using layer-jamming actuation. It assists inspiration by increasing insufflation to mimic diaphragm and intercostal muscle contraction. The positive pressure module exploits soft origami actuators for assistive expiration; it pressures human abdomen and bionically &#x201C;pushes&#x201D; the diaphragm upward. <italic>Results:</italic> The maximum increase in PEF ratios for mannequins, healthy participants, and patients with SCI with robotic assistance were 57.67&#x0025;, 278.10&#x0025;, and 124.47&#x0025;, respectively. The soft exoskeleton assisted one tetraplegic SCI patient to cough up phlegm successfully. <italic>Conclusion:</italic> The experimental results suggest that the proposed soft exoskeleton is promising for assisting the expectoration ability of SCI patients in everyday life scenarios. <italic>Significance:</italic> The proposed soft exoskeleton is promising for advancing the application field of rehabilitation exoskeletons from motor functions to respiratory functions.