  Topologically nontrivial materials host protected edge states associated with
the bulk band inversion through the bulk-edge correspondence. Manipulating such
edge states is highly desired for developing new functions and devices
practically using their dissipation-less nature and spin-momentum locking. Here
we introduce a transition-metal dichalcogenide VTe$_2$, that hosts a charge
density wave (CDW) coupled with the band inversion involving V3$d$ and Te5$p$
orbitals. Spin- and angle-resolved photoemission spectroscopy with
first-principles calculations reveal the huge anisotropic modification of the
bulk electronic structure by the CDW formation, accompanying the selective
disappearance of Dirac-type spin-polarized topological surface states that
exist in the normal state. Thorough three dimensional investigation of bulk
states indicates that the corresponding band inversion at the Brillouin zone
boundary dissolves upon CDW formation, by transforming into anomalous flat
bands. Our finding provides a new insight to the topological manipulation of
matters by utilizing CDWs' flexible characters to external stimuli.
