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In this paper, we propose a novel two-stage based uplink channel estimation strategy with reduced pilot overhead and error propagation for a reconfigurable intelligent surface (RIS)-aided multi-user (MU) millimeter wave (mmWave) system. Specifically, in Stage I, with the carefully designed RIS phase shift matrix and introduced matching matrices, all users jointly estimate the correlation factors between different paths of the common RIS-base station (BS) channel, which achieves significant multi-user diversity gain. Then, the inherent scaling ambiguity and angle ambiguity of the mmWave cascaded channel are utilized to construct an ambiguous common RIS-BS channel composed of the estimated correlation factors. In Stage II, with the constructed ambiguous common RIS-BS channel, each user uses reduced pilots to estimate their specific user-RIS channel independently so as to obtain the entire cascaded channel. The theoretical number of pilots required for the proposed method is analyzed and the simulation results are presented to validate the effectiveness of this strategy.