  We carried out new $^{12}$CO($J$ = 1-0, 3-2) observations of a N63A supernova
remnant (SNR) from the LMC using ALMA and ASTE. We find three giant molecular
clouds toward the northeast, east, and near the center of the SNR. Using the
ALMA data, we spatially resolved clumpy molecular clouds embedded within the
optical nebulae in both the shock-ionized and photoionized lobes discovered by
previous H$\alpha$ and [S II] observations. The total mass of the molecular
clouds is $\sim$$800$ $M_{\odot}$ for the shock-ionized region and $\sim$$1700$
$M_{\odot}$ for the photoionized region. Spatially resolved X-ray spectroscopy
reveals that the absorbing column densities toward the molecular clouds are
$\sim$$1.5$-$6.0\times10^{21}$ cm$^{-2}$, which are $\sim$$1.5$-$15$ times less
than the averaged interstellar proton column densities for each region. This
means that the X-rays are produced not only behind the molecular clouds, but
also in front of them. We conclude that the dense molecular clouds have been
completely engulfed by the shock waves, but have still survived erosion owing
to their high-density and short interacting time. The X-ray spectrum toward the
gas clumps is well explained by an absorbed power-law or high-temperature
plasma models in addition to the thermal plasma components, implying that the
shock-cloud interaction is efficiently working for both the cases through the
shock ionization and magnetic field amplification. If the hadronic gamma-ray is
dominant in the GeV band, the total energy of cosmic-ray protons is calculated
to be $\sim$$0.3$-$1.4\times10^{49}$ erg with the estimated ISM proton density
of $\sim$$190\pm90$ cm$^{-3}$, containing both the shock-ionized gas and
neutral atomic hydrogen.
