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Joint transceiver beamforming is a fundamental and crucial research task in the field of signal processing. Despite extensive efforts made in recent years, the joint transceiver beamforming of frequency diverse array (FDA)-based multiple-input and multiple-output (MIMO) radar has received relatively less attention and is confronted with some tricky challenges, such as range–angle decoupling and the interaction between multiple performance metrics. In this paper, we initially derive the generalized ambiguity function of the FDA-MIMO radar to explore the intrinsic correlation between its waveform design and resolution. Following that, the joint beamforming optimization is formulated as a nonconvex bivariate quadratic programming problem (NBQP) with the aim of maximizing the Signal-to-Interference-Noise Ratio (SINR) of the FDA-MIMO radar system. Building upon this, we introduce an innovative alternating manifold optimization with nested iteration (AMO-NI) algorithm to address the NBQP. By incorporating manifold optimization into iterative updates of transmit waveform and receiving filter, the AMO-NI algorithm considers the interdependencies among the optimization variables. The algorithm efficiently and expeditiously finds global optimum solutions within a finite number of iterations. Compared with other methods, our approach yields a superior beampattern and higher SINR. [ABSTRACT FROM AUTHOR]