An R-matrix calculation is reported for low energy electron collision with the BeO molecule at its equilibrium bond length Re = 2.515 $a_0$ for incident energies below 15 eV. Using a suitably constructed model to represent the BeO target, detailed scattering calculations are performed to obtain cross sections for many collision processes, namely total cross sections for elastic scattering and electronic excitations to some of its low lying states and cross section for electron impact dissociation. Additionally, we have also calculated differential cross sections for electronic excitations from the X 1Σ+ ground state to the first two excited states of the target BeO molecule. BeO is likely to be present as an impurity component in the plasma of fusion devices operating with beryllium as first wall material. We therefore expect the present study to be of substantial importance to the fusion community.