We report a new doorway mechanism for the dissociative electron attachment to genetic materials. The dipole-bound state of the nucleotide anion acts as the doorway for electron capture in the genetic material. The electron gets subsequently transferred to a dissociative σ*-type anionic state localized on a sugar-phosphate or a sugar-nucleobase bond, leading to their cleavage. The electron transfer is mediated by the mixing of electronic and nuclear degrees of freedom. The cleavage rate of the sugar-phosphate bond predicted by this new mechanism is higher than that of the sugar-nucleobase bond breaking, and both processes are considerably slower than the formation of a stable valence-bound anion. The new mechanism can explain the relative rates of electron attachment induced bond cleavages in genetic materials.