The interaction between shock waves and the tip clearance flow in a transonic compressor rotor has important effects on the tip clearance flow and the rotor aerodynamic performance. In this paper, two transonic rotors with a high pressure ratio are selected to study the tip flow, one of which has one normal shock wave at the blade tip and the other has two shock waves (an oblique shock wave and a normal shock wave) at the tip. The two rotors have the same meridional flow channel, design point flow rate, pressure ratio, and rotation speed to focus on the influence caused by the effect of the shock wave structure. The numerical results for the flow fields show the following conclusions. The strength of the two shock waves at the blade tip is weaker than that of one normal shock, and the former two shock waves are less stable than the latter. Therefore, with increasing tip clearance, the efficiency, pressure ratio, and stall margin of the rotor with the two shock waves decrease more rapidly. The static pressure difference between the pressure and suction sides of the tip clearance is the only driving factor of the tip clearance leakage flow, and the leakage flow depends on the local pressure difference and the secondary leakage caused by adjacent blades. The movement speed of the annular wall is less than that of the leakage flow, which has a minor blocking effect on the tip clearance leakage flow. The change in tip clearance has little effect on the chordal distribution of the static pressure difference and leakage flow rate per unit area, so the total leakage flow varies linearly with the tip clearance size.