We carried out new 12CO(J = 1-0, 3-2) observations of a N63A supernova remnant (SNR) from the LMC using the Atacama Large Millimeter/submillimeter Array (ALMA) and Atacama Submillimeter Telescope Experiment. 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 and S ii observations. The total mass of the molecular clouds is ∼800 M☉ for the shock-ionized region and ∼1700 M☉ for the photoionized region. Spatially resolved X-ray spectroscopy reveals that the absorbing column densities toward the molecular clouds are ∼(1.5-6.0) × 1021 cm−2, which are ∼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 model or a high-temperature plasma model, in addition to thermal plasma components, implying that the shock-cloud interaction is efficiently working for both cases through the shock ionization and magnetic field amplification. If the hadronic gamma-ray is dominant in the GeV band, the total energy of the cosmic-ray protons is calculated to be ∼(0.3-1.4) × 1049 erg, with an estimated interstellar proton density of ∼190 90 cm−3, containing both the shock-ionized gas and neutral atomic hydrogen.