Spin excitations in zigzag graphene nanoribbons are studied when the system is subjected to an electric field in the transversal direction. The magnetic properties and the lifetime of the spin excitations are systematically investigated and compared using a tight-binding electron-electron model treated by a mean-field Hubbard model. The effects of electron-hole asymmetry introduced by next-nearest neighbor hopping are also investigated. We show that by increasing the electric field, the antiferromagnetic correlations between the edges of the nanoribbons are decreased due to a reduction of the magnetic moments. The results show that the spin wave lifetime may be controlled by the intensity of the transversal electric field, indicating that zigzag nanoribbons may be considered great candidates for future spintronic applications.