Is the excitation and de-excitation of an electron from the ground state (of an atom) due to the collision of another particle (e.g. electron) an elastic collision or an inelastic collision.

It is an elastic collision. This is because, when a particle collides with the electron of an atom, a discrete amount of energy is transferred from the particle to the electron. This discrete amount of energy is enough for the electron to excite to another discrete energy level. When the electron de-excites, it releases a photon with energy equal to the discrete amount of energy which was used to excite the electron. As no energy is lost during this process, the excitation and de-excitation of the electron is an elastic collision.