The invention relates to a demountable sleeve grouting connection design and construction method which comprises the following steps: providing a sleeve grouting connection design method, and selecting demountable sleeves and accessories with matched sizes according to the diameters of reinforcements; mounting pre-embedded reinforcements in a first sleeve body, connecting a second sleeve body withthe first sleeve body integrally, binding the embedded reinforcements to form a reinforcement cage, performing concrete pouring to obtain a prefabricated member, mounting to-be-connected reinforcements in the second sleeve body, pouring grouting material from a grouting hole, plugging a grout drain hole and a grouting hole after grout is drained from the grout drain hole to form sleeve grouting connection; and during dismounting, separating the sleeve grouting connection from concrete, cutting off sleeve outer reinforcements, separating the sleeves, extruding the sleeve outer reinforcements and integrally draining the sleeve outer reinforcements along with the grouting material from the sleeves, and recovering and maintaining the sleeves and the accessories. The sleeves can be used twiceor multiple times, the types and the quantities of building wastes in the dismounting process of precast concrete members are reduced, resources are saved, and the environment is protected.