No real centrifugal compressor performance exactly conforms to its design geometry and expected operating conditions due to the uncertainties existing in the manufacturing and in-service process. The compressor performance can be adversely affected by such uncertainties and performs instability. However, relevant studies concerning geometric and operational uncertainties simultaneously are quite rare, and the underlying flow mechanism even remains unknown. Here we present both deterministic and uncertainty analysis of a centrifugal compressor stage with considering geometric and operational uncertainties simultaneously. With the combination of CFD simulation and nonintrusive sparse grid based stochastic collocation methods, the combined and single effects of total inlet temperature, total inlet pressure, outlet mass flow, impeller tip clearance and hub fillet radius on the stage/impeller performance are quantified and analysed. The results show that these uncertainties exert more influence on stage rather than impeller performance, therein the uncertain tip clearance contributes the most. To investigate such declined performance indeed, the flow field was then uncovered. It is demonstrated that the wake of tip clearance produces distorted flow downstream towards the diffuser, which causes complicated vortex structures. This present study lays a theoretical foundation to provide guidelines for developing a robust design of centrifugal compressor.