The paper reports a numerical investigation on the dynamic behaviour of a vehicle driveline, equipped with a Torsional Vibration Damper (TVD) based on Magneto-Rheological Elastomeric (MRE) spring elements, during the start-up transient considering an abrupt manoeuvre of clutch engagement. The TVD device consists of a flywheel and a damper disk, with interposed some elastomeric samples which react for relative angular displacements of the two disks. The dynamical parameters of the TVD can be properly tuned by varying the magnetic field surrounding the MRE springs to mitigate the torsional oscillations of the flywheel, causes of many undesired inconveniences as critical speeds or vibro-acoustic issues. The present study promotes the use of the MRE torsional vibration damper to reduce the annoying vibroacoustic phenomenon of “gear rattle” arising in the unloaded gear pairs of the gear box, during and after the rapid clutch engagement transients in the vehicle start-up phase and is conducted on a simplified automotive driveline equipped with a dry clutch. The possibility of quickly tuning the mechanical properties of the MRE-TVD, makes this device particularly eligible for suppressing the above disturbance, adapting to the various operative conditions of the automotive driveline. Results of the analysis, by the help of a Gear Rattle Index (GRI), demonstrate the effectiveness of the proposed device in reducing the vibroacoustic phenomenon during the transient phases of the vehicle start-up, until the vehicles speed conditions are reached.