<p>In this article, we propose two semi-implicit Fourier pseudo-spectral methods to compute the ground state (GS) of rotating Bose-Einstein condensates (BECs) via solving the correlated projected gradient flow (PGF). Different from existing schemes, in our approach, the Lagrange multiplier (LM) in the PGF, which admits an explicit formula that guarantees the mass-preserving and energy-diminishing properties of the PGF at a continuous level, is treated as a new ’unknown’. Henceforth, the PGF is transformed to a system of gradient flow with the ’unknown’ LM and an algebraic equation characterizing the mass-conservation. Integrating with the Fourier pseudo-spectral method for spatial discretization, two semi-implicit schemes are then proposed to discretize the coupled differential-algebraic system. Existences of the solutions of the two full-discretized systems are proved. In addition, both of the two schemes can be solved efficiently in a decoupled strategy. Moreover, we rigorously prove that both schemes preserve exactly the mass, meanwhile decreasing the original total energy at a discrete level for any fixed time step under reasonable conditions. Finally, ample numerical examples are provided to compare the performance of the two schemes and to study the GS of rotating BECs in two-dimensions under different settings.</p>