Geological strength index GSI, disturbance factor (D), material constant mi, and uniaxial compressive strength σci of the intact rock are essential input parameters IPs of the Hoek–Brown H−B criterion. Mechanical parameters MPs of the engineering rock mass, including elastic modulus E, cohesion c, and internal friction angle φ estimated by the H–B criterion, and the predicted excavation response of surrounding rock, including the displacement and excavation damage zone EDZ based on the MPs, are of high relevance with the four IPs of the H–B criterion. In this paper, the deep and huge underground cavern excavated in basalt from a hydropower station under construction in the southwest of China is used to analyse the sensitivity of the IPs on the MPs, the displacement, and EDZ of the surrounding rock mass. Firstly, the H–B criterion is applied to estimate the MPs, among which the IPs are obtained from a series of in situ and laboratory tests, including borehole camera observation, wave velocity test, uniaxial and triaxial compression tests, and so on. Secondly, the sensitivity relationships between IPs, MPs, and prediction results of displacement and EDZ are established and described quantitatively by the sensitivity factor (si). Results show that the MPs of the rock mass are more sensitive to GSI and D⋅GSI and σci are high-sensitivity parameters affecting the displacement and EDZ. Finally, the variations in the estimated MPs and associated prediction results concerning excavation response, which are caused by the uncertainties in the determination of the IPs, are further quantified. This study provides a straightforward assessment for the variability of the rock mass parameters estimated by the H–B criterion. It also gives a valuable reference to similar geotechnical engineering for the determination of rock mass parameters in the preliminary design.