  We show that strong electronic repulsion transforms a vortex core from a
metallic-type in overdoped regime to a Mott-insulator at underdoping of a
strongly correlated d-wave superconductor. This changeover is accompanied by an
accumulation of electron density at the vortex core towards local half-filling
in the underdoped region, which in turn facilitates the formation of the Mott
insulating core. We find that the size of vortices evolves non-monotonically
with doping. A similar non-monotonicity of critical field $H_{\rm c2}$, as
extracted from superfluid stiffness, is also found. Our results explain some
recent experimental puzzles of cuprate superconductors.
