The diversity-multiplexing tradeoff (DMT) of a multiple-input multiple-output (MIMO) multiple-access system is analyzed, where a successive cancellation (SC) receiver is employed. In order to analyze the asymptotic performance of each user in a practical MIMO multiple-access system, we derive the per-user DMT considering error propagation due to imperfect cancellation of the SC process. The diversity gain of each user is shown to be expressed as a simple function of the multiplexing gains of the previously detected users as well as its own multiplexing gain. Also, we show that the diversity gain of each user who suffers from error propagation is strictly smaller than that under the assumption of perfect cancellation in a range of multiplexing gains of the users. Numerical results show that our DMT analysis matches well with the performance of practical multiple-access systems.