The fast ignition (FI) scheme by energetic beams of light ions is one of the main approaches to increase the energy yield in an inertial fusion plasma. In this paper, the injection of a deuteron beam as a suitable laser-drivenignitor is suggested in a helium-3–lithium-6 ($^3$He–$^6$Li) plasma for FI as well. The deuteron beam slows down and deposits its energy through Coulomb and nuclear interactions. The nuclear interaction effect caused by the deuteron beam is investigated on the slowing-down process of field ions. The deuterons can fuse with field ions (both $^3$He and $^6$Li) into plasma as they slow down and provide the added energy yield. The estimation of added energy yield and the evaluation of dependent parameters have a key role in the FI of this fuel with a high fusion yield. The curvature is created in the velocity distribution function due to the nuclear interaction of the deuteron beam in high energy. Reactivity improves at low electron density and high injection energy, compared with the Maxwellian state. Temperature increase reduces the share of nuclear interaction on the slowing-down process. The result indicates that the deuteron beam adds energy to the slowing down component through nuclear interaction. This enhancement of energy is more significant for low densities at high bulk temperature and injection energy. The added energy yield rises with the electron temperature and for ED > 4000 keV decreases with increasing deuteron injection energy. The added yield is high when the deuteron energy is low and the electron temperature is high. The maximum yield occurs with a deuteron beam energy of about 4 MeV. For ED = 4 MeV, the total deposited energy E$_{total^3He+^6Li}$ is about 5.4 MeV at Te = 200 keV and is 6 MeV and 7.08 MeV at Te = 400 keV and Te = 600 keV, respectively. The application of deuteron beam decreases the ignition energy released in the $^3$He–$^6$Li fusion plasma.