Molecular dynamics computer simulations have been employed to investigate the effect of substrate thickness on the ejection mechanism of phenylalanine molecules deposited on free-standing graphene. The system is bombarded from the graphene side by 10 keV C_{60} projectiles at normal incidence and the ejected particles are collected both in transmission and reflection directions. It has been found that the ejection mechanism depends on the substrate thickness. At thin substrates mostly organic fragments are ejected by direct collisions between projectile atoms and adsorbed molecules. At thicker substrates interaction between deforming topmost graphene sheet and adsorbed molecules becomes more important. As this process is gentle and directionally correlated, it leads predominantly to ejection of intact molecules. The implications of the results to a novel analytical approach in Secondary Ion Mass Spectrometry based on ultrathin free-standing graphene substrates and a transmission geometry are discussed.