Given that Mormon chapels (at least modern ones) tend not to have crosses, that Mormons tend not to wear them, and that the cross generally takes second place to Gethsemane in Mormon Atonement theology, speaking of a Mormon theology of the cross might seem a bit odd.  Nevertheless, I believe that the Mormon concept of restoration resonates deeply with Paul’s theology of the cross in 1 Corinthians.
Recall that in writing to the Corinthians Paul is addressing the problem of schism (see 1:10). Among the problems creating division among the Corinthian saints was class distinction: at their Eucharistic feasts, the poorer members would go hungry, while the wealthier had enough wine to get drunk (see 11:18-21).
Paul works to counter this problem right from the outset of his letter:
For Christ did not send me to baptize but to proclaim the gospel, and not with eloquent wisdom, so that the cross of Christ might not be emptied of its power. For the message about the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God. (1:17-18, NRSV)
With “eloquent wisdom” Paul alludes to something that Greek culture privileged, only to dismiss it in favor of the cross, which, Paul insists, appears as foolishness.
Why foolishness? The Greek gods may not have been moral exemplars, but they were powerful. One messed with them at one’s peril. Instead of such gods, Paul preaches the scandal of a crucified God:
For Jews demand signs and Greeks desire wisdom, but we proclaim Christ crucified, a stumbling block [Greek skandalon] to Jews and foolishness to Gentiles, but to those who are called, both Jews and Greeks, Christ the power of God and the wisdom of God. (1:22-24, NRSV)
It’s important to remember that “Christ” here is not a name, but a title, “Messiah.” If the Messiah is one who saves, a Messiah hanging dead on a cross is indeed foolishness. Not only far from wielding the incendiary power of Zeus’s thunderbolt, but a country mile from offering even the slightest gesture of human political redemption, a crucified Messiah seems an utterly ludicrous object in which to invest any hope of salvation. The cross, then, subverts fundamental cultural values, privileging a criminal executed by imperial power over Caesar himself. So much for getting to think you’re important just because you’re rich or otherwise culturally privileged.
In Paul’s letter, the Messianic hope is realized through community, achieved in part through the Eucharist:
The cup of blessing that we bless, is it not a sharing in the blood of Christ? The bread that we break, is it not a sharing in the body of Christ? Because there is one bread, we who are many are one body, for we all partake of the one bread. (10:16-17, NRSV)
Just as the Messiah’s body was broken on the cross—and broken again symbolically in the sacramental bread—Paul calls the community to reunite the body in itself through a collective act of eating and drinking. The crucified Messiah should live again in the united members of the church.
He continues this idea of the body of Christ, famously, in the discourse on spiritual gifts in chapters 12-14. Here, too, the scandal of the cross returns, through the privileging of the weak over the strong:
The eye cannot say to the hand, “I have no need of you,” nor again the head to the feet, “I have no need of you.” On the contrary, the members of the body that seem to be weaker are indispensable, and those members of the body that we think less honorable we clothe with greater honor, and our less respectable members are treated with greater respect; whereas our more respectable members do not need this. But God has so arranged the body, giving the greater honor to the inferior member, that there may be no dissension in the body, but the members may have the same care for one another. If one member suffers, all suffer together with it; if one member is honored, all rejoice together with it. (12:21-26, NRSV)
Given the class-based schisms plaguing the Corinthian church, Paul’s language here is wildly idealistic. Under the best of circumstances, human societies tend to leave people out. On the level of basic sociology, groups often achieve cohesion through exclusion. Beyond which, elevating the marginalized can at times result in a case of “Meet the new boss, same as the old boss.” D&C 121:39 gets it right: a little power all too often leads in short order to unrighteous dominion.
The cross, then, inveighs against this tendency, calling Christians again and again to look for the marginalized and left out. Because of the way human societies marginalize people, it’s a job that’s never done. The minute the Christian message stops indicting you on this point is the minute you’ve stopped really paying attention. 
I think that the notion of restoration in Mormonism has the same potential as the cross to interrupt our comfortable assumptions. Continuing revelation means that beyond a few basic truths (e.g., Jesus is the Christ), Mormons can’t really know anything for certain. (See Bruce R. McConkie’s famous statement in the wake of the 1978 revelation.) Rather, we have to balance doing the best we can within the parameters of our current worldviews with returning again and again to the margins, hoping for some messianic disruption. I don’t mean the margins of our thought—though those matter, too—so much as the social margins. People matter more than propositions, and both Paul and Mormonism stand together in valuing collective over individual salvation.
That said, perhaps a better question than “who are we leaving out?” is “who am I leaving out?” Having been called into the body, we must each do our parts, exercising our spiritual gifts for the good of the whole, whose ultimate aim is to reveal the crucified Messiah in the world, restoring the hoped-for image of the ancient church.
Who can I include in Christ, given my gift?
Music: Tallis, “Salvator Mundi,” Hilliard Ensemble
Salvator mundi, salva nos,
qui per crucem et sanguinem redemisti nos:
auxiliare nobis, te deprecamur, Deus noster.
[Savior of the world, save us,
you who through the cross and blood redeemed us:
help us, we pray you, our God.]
 19th century Mormonism was generally comfortable with the cross; Michael Reed argues that the shift away from using crosses has to do with Mormonism’s 20th-century attempt to join mainstream (i.e., Protestant) American culture, which entailed signing on to mainstream anti-Catholicism. See Banishing the Cross: The Emergence of a Mormon Taboo (Independence, MO: John Whitmer Books, 2012). The book also includes pictures of LDS chapels featuring crosses, typically in architectural ways. A recent article suggests, though, that LDS artists are beginning to depict the cross with increasing frequency.
 If you have a screen to read this blog on, you’re privileged.