What happens if we shoot a single photon to a mirror? I understand mirrors absorb a small energy portion of the light and reflect most of it. What happens if we shoot a single photon to a mirror? Would it be reflected?
If the answer is Yes, then I would ask, if the mirror absorbs a portion of the energy of the photon, so the photon should simply stop existing because we cannot have a smaller package of light than a photon.
If the answer is No, then I would ask why a beam of light (which is made of a big number of photons) behaves differently.
 A: Light is composed of photons which have energy $hν$, $ν$ the frequency of the classical light . Photons are elementary particles with mass zero and spin +/-1. In this plot for a polarized beam one can see how the quantum particle photon contributes to the ensemble of photons that make up the classical electromagnetic wave. It is not simple addition.


Left and right circular polarization and their associate angular momenta

A free photon is mathematically represented by a wave packet, i.e. a number of frequencies contribute with a width coming from the creation source.
In this link I describe the interactions a photon can have with a mirror.

I understand mirrors absorb a small energy portion of the light and reflect most of it. What happens if we shoot a single photon to a mirror? Would it be reflected?

Within the width of the photon wave packet, in order to have mirroring the photon has to be reflected, i.e. elastically scattered, keeping the phases with the ensemble in order for reflected  images to be seen. The absorbed energy is very small because the mass of the mirror is very large and the effect is not seen in the image. See the answers here.

If the answer is Yes, then I would ask, if the mirror absorbs a portion of the energy of the photon, so the photon should simply stop existing because we cannot have a smaller package of light than a photon.

The photon per se is not quantized, it can continually lose energy in an interaction. It disappears completely only if its energy fits the energy level of some bound state (atom,molecule,lattice) when it has a probability of raising the energy level of an electron . In the mirror case because the mass of the mirror is very large the reflected photon has lost energy within the limits of its wavepacket.(otherwise it would not be a mirror)
A: When a beam of light hits a mirror, photons are scattered, most of them are elastically scattered (Rayleigh scattering), such that the scattered photons have the same energy (frequency, wavelength, and color). An even smaller fraction ($X$) of the scattered photons can be scattered inelastically, with the scattered photons having an energy different (usually lower) from those of the incident photons. This fraction depends on the mirror efficiency.
Now, if a single photon hits a mirror, there is the chance of ($X$) that it loses part of its energy and reflect (redshifted), and the bigger chance of ($1-X$) that its energy is conserved and reflect.
