The power of the cross is emptied if Jesus took on the sins of the world by bleeding in extreme agony for them in the Garden of Gethsemane. The cross becomes merely a tool to lead to Jesus' death so that he could overcome the grave, rather than the place where God's love poured out in the death of Jesus to pay for our sins.
But God demonstrates his own love for us in this: While we were still sinners, Christ died for us.
This is a physician's analysis of Luke's statement about Christ's sweat being as blood in the Garden of Gethsemane:
"This is a known medical condition called hematidrosis. It's not very common, but it is associated with a high degree of psychological stress. What happens is that severe anxiety causes the release of chemicals that break down the capillaries in the sweat glands. As a result, there's a SMALL amount of bleeding into these glands, and the sweat comes out TINGED with blood. WE'RE NOT TALKING ABOUT A LOT OF BLOOD; IT'S JUST A VERY, VERY SMALL AMOUNT." (The Case for Christ, Lee Strobel, 195, emphasis mine)
Even if Luke's statement of Christ's sweat being as blood was literal and not a simile (comparison), Christ wasn't sweating tons of blood or else he would have made a far more shocking appearance when he finished praying and met the soldiers and Judas Iscariot. It was due to psychological stress--he knew what was coming, and it was obvious he felt extreme trepidation about it, considering that he asked God that the cup might pass from him if it were God's will.
Even from this standpoint of a medical professional, Luke's statement does not in any way mean that Jesus was sweating literal drops of blood because he was suffering for our sins while in the Garden instead of (or in addition to) his suffering on the Cross.
Death was necessary to pay for our sins--why else would animal sacrifice have been done by the priests to cleanse sin in the Old Testament?
1 Corinthians 1:17-18
For Christ did not send me to baptize, but to preach the gospel—not with wisdom and eloquence, lest the cross of Christ be emptied of its power. For the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God.
and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross. (Not his blood shed in the Garden)
having canceled the charge of our legal indebtedness, which stood against us and condemned us; he has taken it away, nailing it to the cross.
1 Peter 2:24
“He himself bore our sins” in his body on the cross, so that we might die to sins and live for righteousness; “by his wounds you have been healed.”
1 Corinthians 15 3-4
For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, that he was buried, that he was raised on the third day according to the Scriptures (notice the Garden is not mentioned, but his death is.)
Contrast this with statements by Mormon General Authorities:
"In the Garden of Gethsemane, He suffered so greatly that he sweat drops of blood as He pleaded with His Father. But this was all a part of His great atoning sacrifice." Gordon B. Hinckley, April 2007 General Conference
"With His divine sonship, His sinless life, the shedding of His blood in the Garden of Gethsemane, His excruciating death on the cross and subsequent bodily resurrection from the grave, He became the author of our salvation and made a perfect Atonement for all mankind."
"His profound suffering in the Garden of Gethsemane, where He took upon Himself all the sins of all other mortals, caused Him “to tremble because of pain, and to bleed at every pore, and to suffer both body and spirit.”"
James E. Faust, October 2001 General Conference
The Garden of Gethsemane at the Mount of Olives