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We present a theory of the deficient spinel compound GaV₄S₈ (GVS) using a cluster DMFT approach. GVS has been of growing interest recently because of its multiferroicity below T_C ~ 13K. At T_f ~ 70K it has an additional structural transition from a cubic to a rhombohedral structure with cooling. Across the two structural transitions GVS remains insulating with a gap of about ~ 0.3 eV, and the insulating nature of its high-temperature cubic paramagnetic phase is suspected to be of Mott type. However, there have been no systematic studies of the Mott-insulating phases of GVS, which should be important for understanding the ferroelectric and multiferroic phases. For this problem, we apply a cluster DMFT method that treats selected atomic orbitals on a cluster of four V atoms, using a molecular orbital basis set instead of an atomic one. Comparing with single-V-site DMFT calculations, we show that intra-cluster correlations are essential in reproducing the Mott-insulating nature of the high-T cubic paramagnetic phase. Correlation effects on the crystal structure of GVS will be also discussed, and the role of Hund's coupling in tuning V clustering by controlling spin-state transitions will be demonstrated.