The magnetic dilution method was employed in order to elucidate the origin of the slow relaxation of the magnetization in a Dy-2 single-molecule magnet (SMM). The doping effect was studied using SQUID and micro-SQUID measurements on a Dy-2 SMM diluted in a diamagnetic Y-2 matrix. The quantum tunneling of the magnetization that can occur was suppressed by applying optimum dc fields. The dominant single-ion relaxation was found to be entangled with the neighboring Dy-III ion relaxation within the molecule, greatly influencing the quantum tunneling of the magnetization in this complex.