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In this paper, we present the diversity-multiplexing tradeoff (DMT) analysis for minimum mean squared error (MMSE) based amplify-and-forward cooperative multiple antenna half-duplex relaying systems where a non-negligible direct link exists between the source and the destination. First, we evaluate an upperbound of the DMT which offers a theoretical limit of the system and show that the upperbound is actually achievable by existing optimal and suboptimal designs for the relay amplifying matrix. Thereby, we establish the optimal DMT for the MMSE-based cooperative relaying system. Our analysis also illustrate the optimality of the conventional relay matrix designs in terms of the DMT and leads to several interesting observations. Finally, numerical simulations demonstrate the accuracy of our analysis.