The present invention relates to the technical field of the device and method of oil-gas mining and drilling well jet, more particularly to a drilling rig of utilization supercritical carbon dioxide and method, which prevents 'ice bag' to produce and efficient rock-breaking, bit speed and clear rock ability is improved simultaneously, make drilling in higher efficiency, the lower utilization supercritical carbon dioxide of cost; Drilling rig includes continuous-tube roller, inner tube drilling pump, outer tube drilling pump, injection head, outer tube, inner tube and drilling well main body; Drilling well main body includes screwed union, screwed union is internally provided with outer tube cavity and inner tube cavity, the side wall of screwed union and bottom are respectively arranged with multiple backward nozzles and multiple forward direction nozzles, screwed union is internally provided with self-oscillation chamber and multiple points of chambers, in multiple points of chambers, the inside in each point of chamber is provided with disc spring group, and disc spring group is arranged on sub-chamber inner sidewall by sealing ring.