Does LDS doctrine explicitly emphasize the atonement in Gethsemane?

A 3-part definition

Preach My Gospel (the instruction manual for the church's missionaries) offers the following definition:

The Savior’s Atonement included His suffering in the Garden of Gethsemane and His suffering and death on the cross, and it ended with His Resurrection. Though He suffered beyond comprehension—so much so that He bled from every pore and asked whether it were possible that this burden be lifted from Him—He submitted to the Father’s will in a supreme expression of love for His Father and for us. This triumph of Jesus Christ over spiritual death by His suffering and over physical death by His Resurrection is called the Atonement of Jesus Christ.

This definition includes:

• His suffering in Gethsemane
• His suffering and death on the cross
• His resurrection

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We notice what is distinct

It is not uncommon for groups to be distinguished by & focus on features that are unique to them. The Church of Jesus Christ of Latter-day Saints' distinct teachings about what took place in the Garden of Gethsemane, then, often do elicit a great deal of attention, because they are different.

It is also true that this painting by Harry Anderson, of Jesus kneeling in Gethsemane, is an absolutely beloved favorite piece of artwork adorning many Latter-day Saint buildings (incidentally, though, Harry Anderson was not a Latter-day Saint).

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Gethsemane

The suffering of Jesus in Gethsemane played an essential role in the Plan of Salvation. Two of the more poignant passages describing this are:

And lo, he shall suffer temptations, and pain of body, hunger, thirst, and fatigue, even more than man can suffer, except it be unto death; for behold, blood cometh from every pore, so great shall be his anguish for the wickedness and the abominations of his people. (Mosiah 3:7)

18 Which suffering caused myself, even God, the greatest of all, to tremble because of pain, and to bleed at every pore, and to suffer both body and spirit—and would that I might not drink the bitter cup, and shrink—

19 Nevertheless, glory be to the Father, and I partook and finished my preparations unto the children of men. (Doctrine & Covenants 19:18-19)

(compare also to Luke 22:44 & Alma 7:11-13)

We believe that in Gethsemane Jesus was not just contemplating with anguish the pains He knew would come a few hours later at the hands of the Romans--Jesus experienced something considerably worse. He took upon Himself all of the pain, all of the sorrow, and all of the grief all of humanity would ever feel. He suffered the penalty for all of humanity's sins.

We believe that Jesus descended below all things (see Doctrine & Covenants 88:6-7, 122:8). Other men have experienced the pains of crucifixion, and other men have sacrificed their lives for another, but no other has borne the pains & the penalties of all of humanity.

Speaking of the events in Gethsemane, James E. Talmage (an apostle of the church) wrote:

Christ’s agony in the garden is unfathomable by the finite mind, both as to intensity and cause...He struggled and groaned under a burden such as no other being who has lived on earth might even conceive as possible. It was not physical pain, nor mental anguish alone, that caused Him to suffer such torture as to produce an extrusion of blood from every pore; but a spiritual agony of soul such as only God was capable of experiencing...In that hour of anguish Christ met and overcame all the horrors that Satan...could inflict (Jesus the Christ p.613).

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The cross

The death of Jesus on the cross played an essential role in the Plan of Salvation; His anguish & sacrifice were certainly not complete after Gethsemane.

This emphasis is clearly found in the Book of Mormon. For example:

13 Behold I have given unto you my gospel, and this is the gospel which I have given unto you—that I came into the world to do the will of my Father, because my Father sent me.

14 And my Father sent me that I might be lifted up upon the cross; and after that I had been lifted up upon the cross, that I might draw all men unto me, that as I have been lifted up by men even so should men be lifted up by the Father, to stand before me, to be judged of their works, whether they be good or whether they be evil (3 Nephi 27:13-14)

It is also found in our hymns, including:

• Upon the Cross of Calvary
• In Memory of the Crucified
• There Is a Green Hill Far Away

Many additional scriptures & hymns could be cited.

Some wonder why Latter-day Saints do not (usually) wear a cross nor adorn their buildings with crosses. There is a separate question on this site addressing this topic, including the following statement by former church President Gordon B. Hinckley:

I do not wish to give offense to any of my Christian colleagues who use the cross on the steeples of their cathedrals and at the altars of their chapels, who wear it on their vestments, and imprint it on their books and other literature. But for us, the cross is the symbol of the dying Christ, while our message is a declaration of the Living Christ.

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the lives of our people must become the most meaningful expression of our faith and, in fact, therefore, the symbol of our worship. (source)

The absolute centrality of what happened on the cross was underscored by apostle Jeffrey R. Holland:

Now I speak very carefully, even reverently, of what may have been the most difficult moment in all of this solitary journey to Atonement. I speak of those final moments for which Jesus must have been prepared intellectually and physically but which He may not have fully anticipated emotionally and spiritually—that concluding descent into the paralyzing despair of divine withdrawal when He cries in ultimate loneliness, “My God, my God, why hast thou forsaken me?”

...that the supreme sacrifice of His Son might be as complete as it was voluntary and solitary, the Father briefly withdrew from Jesus the comfort of His Spirit, the support of His personal presence. It was required, indeed it was central to the significance of the Atonement, that this perfect Son who had never spoken ill nor done wrong nor touched an unclean thing had to know how the rest of humankind—us, all of us—would feel when we did commit such sins. For His Atonement to be infinite and eternal, He had to feel what it was like to die not only physically but spiritually, to sense what it was like to have the divine Spirit withdraw, leaving one feeling totally, abjectly, hopelessly alone. (source)

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Conclusion

• Do Latter-day Saints place tremendous emphasis on what happened in Gethsemane? Yes
• Do Latter-day Saints treat as secondary or separate-from-the Atonement Jesus' death on the cross? No

The Atonement of Jesus Christ & how it transforms us is the central message of the Book of Mormon. Through His sacrifice at Gethsemane and Golgotha, Jesus perfectly understands our every struggle, and has made an infinite & eternal atoning sacrifice for all mankind.

Disclaimer: my comments are the product of my own study and do not constitute official statements by The Church of Jesus Christ of Latter-day Saints.