the Elysian Mysteries, page 1

In terms of the actual particulars of the Mysteries themselves, we are unfortunately forced to utilise assumption and guesswork, given that the Mysteries were ... well ... mysteries.

I highly doubt that the rites themselves involved the literal sacrifice of virgins in a re-enactment or literalisation of the Persephone-Hades descent myth. The reason I say this is because a critical element in the myth itself involves the rebirth of Persephone herself from the lands of the dead. Remember, it was not Persephone who made the land fertile, but rather her mother, Demeter, who only caused the crops to grow on seeing her daughter's arrival back in the land of the living. In this context, the way in which the Earth's fertility would be restored would be for the virgins to die and then be reborn. Given this, I find it much more likely that initiates into the Mysteries underwent a symbolic death and resurrection to reaffirm, if you will, the act of Persephone's own death and rebirth. The initiation rite itself probably involved the use of mind-altering substances to induce a state in which the initiate was perceived to be dead and in which the initiate received visions that would be interpreted in the context of the rites.

Such symbolic death and rebirth rituals are common in initiation rituals. Amongst many Australian Aboriginal peoples, for example, an initiate underwent a staged death and rebirth to learn the training and education deemed necessary by their elders:

Initiation in Aboriginal Australia was a symbolic reenactment of death in order to achieve new life as an adult. As a novice left his camp, the women would wail and other noises would be made, symbolizing the voice of a mythic being who was said to swallow the novice and later vomit him forth into a new life. The initiation rites themselves were a focal point in discipline and training; they included songs and rituals having an educational purpose. All boys were initiated, and traditionally there were no exceptions.

Reference

Similar rites can be found in cultures throughout the world.

It is also important to note that, whilst we do know that the Mysteries did involve sacrifice, the sacrifice was one of animals - in this case a pig (in the Lesser Mysteries and again at the start of the Greater Mysteries) and a bull (at the Pannychis near the end of the Greater Mysteries) (Reference). The sacrifice was not human in nature.

The Mysteries were used as a celebration of Persephone's death and rebirth and the subsequent renewal of the seasons that occurred as a result. They came about as a result of the legend, not the other way around. This is revealed to us through the Homeric Hymn to Demeter, which was a poem believed to have been based on the Mysteries themselves in which it states that Demeter:

went, and to the kings who deal justice, Triptolemus and Diocles, the horse-driver, and to doughty Eumolpus and Celeus, leader of the people, she showed the conduct of her rites and taught them all her mysteries, to Triptolemus and Polyxeinus and Diocles also, -- awful mysteries which no one may in any way transgress or pry into or utter, for deep awe of the gods checks the voice. Happy is he among men upon earth who has seen these mysteries; but he who is uninitiate and who has no part in them, never has lot of like good things once he is dead, down in the darkness and gloom.

Reference

This same quote shows us that death was reserved not for those who stumbled upon the rites, but for initiates who revealed the Mysteries to the uninitiated (Reference).

Descent motifs such as that of Persephone are common throughout the mythology of the ancient world. Similar stories are: Inanna's Descent Into the Underworld and the Ressurection of Osiris.