Revisited after some negative votes.
The photon is an elementary particle in the standard model of particle physics. This means it is a quantum mechanical "particle" described by a wavefunctions which will give for any interaction the probability of a specific photon to interact. In the case of a mirror, ray optics describe the most probable path of a photon before and after an interaction.
As a particle, when hitting matter in solid state it may scatter elastically with the collective electric field of the medium it hits, To have a mirror all photons must scatter elastically from the solid state lattice that is the mirror.
Elastically means that the photon leaving an interaction only changes direction in the center of mass. The center of mass of a photon and a mirror is effectively the laboratory frame as the mirror is of order ~10^23 molecules in mass. Thus the elastically scattered photon does not lose energy, and the colors of the images it helps to build up do not change. How classical states emerge from the underlying quantum field theory state is described here.
A photon will be absorbed if its energy, given by $E=h\nu$, fits some energy level of the atoms, (molecules, system) it hits and then a re-emitted photon may change both direction and energy with respect to the originating one, i.e. if the reflected one changes frequency because of the re-emission,and loses the phase it cannot contribute to a faithful image. The photon of course goes with velocity $c$ (as all photons) whatever its direction (elastic scattering means only change of direction and not energy).
The diagrams describing photon scattering are similar in first order to the ones below,
where the electrons are virtual, interacting with the mirror lattice and the outgoing photons have the same frequency/energy.
In elementary particles "same" can only have the meaning on specific variables in specific interactions. In elastic scattering the photon entering the interaction and the photon leaving have the same frequency (energy) and each photon has a probability to be scattered at an angle. The classical wave built up by the zillions of photons in superposition of their wavefunctions have to keep the phases so that the macroscopic images can keep their color and dimension, i.e. be "mirrored".