Given some of the comments in this question, I feel compelled to ask: "Does Mormonism constitute a present-day example of a mystery religion?" I'm interested in both insider and outsider perspectives.
The article states that Christianity itself, particularly as it originally existed in the days of the early Church, meets the definition of a mystery religion, and that this was noted and remarked upon by one of the great early apologists, Justin Martyr. And if the definition is that "participation is reserved to initiates," then Judaism meets the definition as well: Gentiles who had not converted could not take part in many of its sacred rituals, particularly ones that involved the Temple. The Temple had an outer area known as the court of the Gentiles where outsiders could come, but beyond that, they were not welcome.
The Church of Jesus Christ of Latter-Day Saints claims to be the restoration of original Christianity, so it's not surprising to see such features as part of its theology. Participation in sacred temple ordinances is "reserved to initiates," as the article describes it, and certain matters regarding temple ceremonies are not to be discussed outside of the temple.
However, there is an important distinction to understand: to Latter-Day Saints, these matters are not secret; they are sacred. I explained the difference in this question: the value of a secret is in exclusivity, whereas Latter-Day Saints actively invite and work to persuade all to come to the temple, but only once certain standards of preparedness, understanding, and spiritual maturity have been met.
Forgive me for commenting over a year after the question was asked. I am a Mormon, and I consider myself to be passionate not only for my own faith, but for religion in general. My current religious obsession is in the Greco-Roman mystery religions, particularly those claiming authority from Orpheus. The more I learn of these faith traditions, the more I'm staggered by the similarities I see in my own faith. In the LDS temples, as in the mystery ceremonies of old, we make oaths and promises to ensure a good afterlife, we are sworn to secrecy (to a degree), and we learn sacred tokens, passwords, and instructions for use after our physical death. One major difference between ancient mystery cults and Mormonism is that, though we are threatened by spiritual damnation for revealing our temple practices, we are not under threat of death for doing so. Those who have no fear of damnation have revealed the aesthetic layer of our practices, and so the respectful silence of the ancient cults has sadly eluded us.
It's not necessary to attend the temple or participate in temple ordinances in order to belong to the LDS church. One merely needs to be baptized by someone holding the Aaronic priesthood to be considered a Mormon. Temple ceremonies are completely optional, and (ideally) dependent on personal worthiness. For these reasons, I would say that Mormonism is similar to the ancient mystery religions, but isn't necessarily a mystery religion itself.
In response to the prior answer of Mormonism not putting practitioners under threat of death for talking about temple practices, while that is true of the current temple endowment ritual, that was not true of the original endowment ritual.
It is well known to scholars of Mormon religious history, that the original Temple Endowment ceremony in 1842, Joseph Smith instituted Penalty, and Execution Penalty segments at multiple points in the Temple Endowment Ceremony. These portions comprised of saying phrases and gestures that indicated that the penalty for revealing the temple ceremonies was to be death.
These portions of the endowment ceremony were modified to be less graphic by Mormon Church President Heber J. Grant from the years 1919-1927, and were removed entirely from the endowment ceremony in 1990.
So while it's true that the modern temple endowment does not follow that mystery religion practice, any Mormon member who received their endowment prior to 1990 had undergone a watered-down and slightly sanitized version of a mystery religion death oath.
It can also be reasonably inferred that Mormonism from 1842 inwards was effectively a full mystery religion, and that in the ensuing decades it has taken active steps to water-down and distance itself from some of the more extreme mystery religion practices since.
That being said, realistically a form of the death oath was present in the endowment ceremony a mere 28 years ago, so while Mormons under the age of 48 can't be expected to be aware of this practice, any faithful Mormon adherent from the age of 48+ can likely be expected to have fully participated in what can reasonably defined as a fully mystery religion experience, threat of bodily harm for exposing the ritual included.
All of this information is rather easy to look up and confirm, either by talking to a friendly older Mormon member who is willing to talk about the temple changes, or by a quick google search on the changes in the Mormon Endowment Ceremony. These changes are so well-recorded that my primary source for this response was a wikipedia article on the subject. (that can be verified by multiple more scholarly articles, should need arise)
In terms of perspective, count me as a "formerly inside, currently outside" perspective. I was raised Mormon, and went through the endowment ceremony around 2001. At one point my Mom alluded to the fact that she was very, very happy that I didn't have to go through the death oath portion of the ceremony that she had had to growing up. That being said, I didn't learn about the full details of the changes to the temple ceremony in 1990 until well after I had left that faith, as despite the fact that the official party line is "sacred not secret" the practical upshot of holding important religious ideas that "sacred" is that they are almost never talked about, limiting the ability of even active members from having a full understanding of their own religious history.