Vanadium dichalcogenides have attracted increasing interests for the charge density wave phenomena and possible ferromagnetism. Here, we report on the multiphase behavior and gap opening in monolayer VTe₂ grown by molecular beam epitaxy. Scanning tunneling microscopy (STM) and spectroscopy study revealed the (4×4) metallic and gapped (2 $\sqrt{3}$ ×2 $\sqrt{3}$ ) charge-density wave (CDW) phases with an energy gap of ~ 40 meV. Through the in-plane condensation of vanadium atoms, the typical star-of-David clusters and truncated triangle-shaped clusters are formed in the (4×4) and (2 $\sqrt{3}$ ×2 $\sqrt{3}$ ) phases respectively, resulting in different surface morphologies and electronic structures as confirmed by density functional theory (DFT) calculations with on-site Coulomb repulsion. The CDW-driven reorganization of the atomic structure weakens the ferromagnetic superexchange coupling and strengthens the antiferromagnetic exchange coupling on the contrary, suppressing the long-range magnetic order in monolayer VTe₂. The electron correlation is found to be important to explain the gap opening in the (2 $\sqrt{3}$ ×2 $\sqrt{3}$ ) phase.