Mithraism was particularly a male-only cult that proliferated amongst the legions of the Roman Empire. Riding into the Battle at Milvian Bridge in 312 BCE, Constantine had a vision where Jesus proclaimed he would win the battle...and he did. It was common practice after battles and wars to commemorate one's victory with a celebration to any deity that may have aided the victorious army. Constantine did just that, honoring the God of the Christians for blessing him with a victory. With this, soldiers then turned to their new celestial guide and commander, supplanting Mithras with the Christian God. With this, Constantine declared Christianity to be legal cult in Rome, thus it no longer could be lawfully attacked.
In time, Constantine and his successors made laws against various aspects of the Traditional Religion of Rome, what Cicero called the Cultus Deorum Romanorum.
Mithraists held their rites and feasts for Mithras in subterranean enclosures at night. Christians critisized the Mithraists for performing devious rites to demons; in the Roman Religion the only entities approached in ritual in the night are infernal deities and spirits of the Underworld. At some point, a ban was placed on the performance of nocturnal rites and sacrifices, practically halting the Mithraic liturgies from being performed. In time, statues, dedications, subterranean caverns and all the like that pertained to Mithraism were destroyed and Mithraism was effectively wiped out.
The Apologist Firmicus Maternus denounced Mithras by recognizing His origins in Persia, which the Persians were Rome's current enemy. In Rome, it was improper to support divine entities that had origin or were related to the enemy of Rome.
When Theodosius I came to power, he instituted the official ban on all rites, sacrifices, temples and so on that formally pertained to the Traditional Roman Religion. Theodosius ordered the Vestal Virgins to be disbanded, the fire of Vesta extinguished and the Altar of Victory was removed from the Senate House; all of these containing in them the core of Roman Religion.
Theodosius I is the Emperor responsible for eliminating all pre-Christian religions and for instituting Christianity as the State Religion of Rome and the Roman Empire.