Well, you can't make anything like a mirror. You can bounce a few particles off of a shielding material. But different particles will bounce off of atoms in the shielding material at different depths, and as Doug alludes to above, much of the energy that comes back will not be in the muons that make up most of the cosmic rays.
The fundamental problem is that the incoming muons are going so fast that when they interact with any sort of normal matter, they only see a bunch of atomic nuclei swimming in a field of electrons. The electrons will slow the muons down, while they'll have a rather energetic reaction if they strike an atomic nucleus. The specific type of matter will only impact how much the muons are slowed by the electrons, and how likely the muon is to strike a nucleus.
As for the impact on the nucleus, the mean energy of muons at sea level is approximately 4GeV, which is around four proton masses. I don't think it's possible for an atomic nucleus to survive an impact of that magnitude: the combination of the muon and the nucleus would be turned into a shower of particles. That said, most of the time such collisions don't happen: the muon just gets slowed down until it nearly stops, and then it decays into an electron and a pair of neutrinos. Most of the energy escapes via the neutrinos, and the electron rapidly slows.
