The invention relates to an overall replacement system for an original building shock-insulation support and a construction method. According to an overall replacement system structure, four temporary small foundations fall on a structural foundation and are evenly distributed on the periphery of the shock-insulation support, a section steel column is placed on each temporary small foundation, a steel cushion plate is placed on the top of each section steel column, a jack is placed on each steel cushion plate, another steel cushion block is placed on each jack, each another steel cushion block makes contact with the beam bottom, and it is guaranteed that a stress system is safe and reliable; one oil pressure pump is connected with the four jacks; four reversed beams are evenly distributed on the periphery of a beam column joint of an upper supporting pier of the shock-insulation support. In the replacement process of the shock-insulation support, jacking supporting, monitoring and high-pressure water lossless jet cutting are selected to be performed, and it is guaranteed that the construction process is safe, controllable, efficient, environmentally friendly, easy and fast.