Neutron stars (NS) that are born in binary systems, with a main sequence star companion, can experience mass transfer, resulting in the accumulation of material at the NS's surface. This, in turn, leads to the continuous growth of the NS mass and the associated steepening of the gravitational potential. If the central density surpasses the onset for the phase transition from nuclear, generally hadronic matter to deconfined quark-gluon plasma-a quantity currently constrained solely from an upper limit by asymptotic freedom in QCD-the system may experience a dynamic response due to the appearance of additional degrees of freedom in the equation of state (EOS). This might give rise to a rapid softening of the EOS during the transition in the hadron-quark matter co-existence region. Whilst this phenomenon has long been studied in the context of hydrostatic configurations, the dynamical implications of this problem are yet incompletely understood. It is the essence of the present paper to simulate the dynamics of NS, with previously accreted envelopes, caused by the presence of a first-order QCD phase transition. Therefore, the neutrino radiation hydrodynamics treatment is employed based on the fully general relativistic approach in spherical symmetry, implementing three-flavor Boltzmann neutrino transport and a microscopic model EOS that contains a first-order hadron-quark phase transition. The associated neutrino signal shows a sudden rise of the neutrino fluxes and average energies, becoming observable for the present generation of neutrino detectors for a galactic event, and a gravitational wave mode analysis reveals the behaviors of the dominant f and first gravity g modes that are being excited during the NS evolution across the QCD phase transition.