In constructing hard rock mine deep shafts, the failure caused by high stress is a significant problem. A construction section extending from the -930 m to -1271 m level of a 1527 m deep shaft was selected as a case study. Q, RMR, and GSI rock mass quality classifications of the surrounding rock were obtained to determine the shaft’s maximum unsupported sinking cycle height in different construction sections. The potential failure mode, failure zone shape, and failure depth of the surrounding rock shaft under high stress were then analyzed theoretically, empirically, and by numerical simulation, sequential stress control and delayed support technology was proposed according to the results. The temporary and permanent support timing parameters were calculated and verified by the empirical chart, numerical simulation, convergence-confinement theory, and theoretical formula. Results show that the surrounding rock in all the construction sections from -930 m to -1271 m belongs to the mild or severely pressure squeezed strata. The potential failure mode is stress-controlled, and the failure zone of the surrounding rock is “ear” shaped. Temporary support strengthens the rock mass, improves the shear capacity of surrounding rock, and prevents the broken rock from falling but does not release stress. Permanent support, conversely, cannot bear the stress of surrounding rock. The stress and elastic strain energy in rock mass should be released to the greatest extent possible before installing permanent support; it is not advisable to install it too early. The time and cycle height of delayed permanent shaft support were comprehensively determined to be four days and 16 m, respectively. The numerical simulation and safety factor proof show that the sequential stress control process effectively minimizes stress in surrounding rock and ensures long-term shaft stability.