Christ's Atoning Sufferings are what Christ endured on the cross to put away sin in three hours of darkness. At Gethsemane the Lord came to terms with his Father about the cross, but at Calvary He paid the debt. Our minds can only begin to comprehend all the sufferings that came before this awful hour. But that which Christ suffered to make expiation for sin transcends the powers of the human mind, and the confines of the human heart.
Three parts to Atonement. It is important to understand that there are three parts to atonement; the sufferings, death, and blood-shedding. The sufferings of Christ at the hand of God, both to bear the punishment that we deserved and to render a perfect satisfaction to God, were required to make atonement. But if He had come down from the cross after the three hours, atonement still would not be complete. In the death of Christ, we have His whole Person offered up as a sacrifice to God. The death of the Victim was required. Then His blood was shed; blood which contained all the value of His atoning-sufferings and atoning-death. The blood from the scourging, the nail prints, and the crown of thorns was shed before the atoning sufferings and death. It was the blood that flowed from the side of a dead Christ that contained all the value of His sufferings in three dark hours, and all the value of His life offered up to God in death. Atonement could not be accomplished without all three of these components. But the subject at hand is the atoning sufferings, which is the first of the three components.
Two Aspects of the Atoning Sufferings.
One part of His work, called substitution,
dealt with our sins (plural); but there was another part of His work, called propitiation,
that dealt with the whole question of sin (singular) to the glory of God. Read more...
Bearing Our Sins. Our sins were laid upon Christ in a similar way that the sins of the people of Israel were confessed on the head of the sacrifice for a sin offering (Lev. 16:21; Lev. 4). Our sins were transferred to Christ "on the tree", who "His own self" - no other substitute would do - "bare our sins" under the fiery wrath of God "in His own body" (1 Pet. 2:24). Peter goes on to connect Christ's sin bearing with the description in Isa. 53, where in v.5 the Spirit uses four types of physical injuries to picture the atoning sufferings of Christ: wounds, bruises, chastisements, and stripes. In this way "Jehovah hath laid upon him the iniquity of us all" (Isa. 53:6).
Himself a Propitiation. Not only did Christ suffer for our sins, but His soul was made an offering for sin. This is the burnt-offering character of the work of Christ. When sin came into God's creation, a grievous injury was inflicted against the holiness and majesty of God. Sin coming into the creation did not mar or lesson God's holiness, for "light" is His essential character, but it nevertheless slighted His name. God's character must be vindicated. Sin must be put out of His sight, and the effects of sin cleansed from His universe. To meet this demand, Christ offered Himself as a propitiation on the cross. When propitiation is mentioned, it is always connected with Christ offering "Himself" - His whole Person - up as a sacrifice to God. The propitiatory aspect of atonement is all for God, although it was necessary because of our sins (Heb. 2:17; 1 John 2:2; 1 John 4:10). In order to accomplish this, Christ had to be "made sin" for us.
Made Sin for Us. In order to accomplish atonement, Christ had to go into the place of sin; that very thing God hates, which has offended His glory. Christ had to be "made sin" in God's sight, and judged as sin (2 Cor. 5:21). Only a holy God could know the horror of Christ's being made sin, "who knew no sin". With what horror Christ contemplated this prospect in the garden of Gethsemane! There is nothing like it. All the betraying, mocking, and scourging that had been heaped upon Christ cannot be compared to what He suffered as the victim of God's wrath against sin.
“Jesus felt it all; but the anguish of His trial, where after all He was a calm and faithful witness, the abyss of His sufferings, contained something far more terrible then all this malice or abandonment of man. The floods doubtless lifted up their voices. One after another the waves of wickedness dashed against Him; but the depths beneath that awaited Him, who could fathom? His heart, His soul — the vessel of a divine love — could alone go deeper than the bottom of that abyss which sin had opened for man, to bring up those who lay there, after He had endured its pains in His own soul. A heart that had been ever faithful was forsaken of God. Where sin had brought man, love brought the Lord, but with a nature and an apprehension in which there was no distance, no separation, so that it should be felt in all its fulness. No one but He who was in that place could fathom or feel it.” - J.N. Darby 
The Abandonment. The Lord Jesus had said to His disciples on the previous night, Ye “shall leave Me alone; and yet I am not alone, for the Father is with Me” (John 16:32). All the way up until noon on the crucifixion day (the sixth hour), the Lord Jesus was able to enjoy perfect communion with His Father. "The eternal God is thy refuge, and underneath are the everlasting arms" (Deut. 33:27). But during the three hours of darkness, from the sixth to the ninth hour, while Christ was made sin and judged for it, He was abandoned by His God. God is "holy, holy, holy" (Isa. 6:3). "God is light, and in him is no darkness at all" (1 John 1:5). Iniquity is what separates man from his God (Isa. 59:2), because God can have no sin in His presence. Therefore, God had to turn His face away from His suffering Servant. Although Christ was suffering to bring Him glory, God nevertheless forsook Him - abandoned Him - in those three dark hours. At the close of the three hours we hear those awful words;
“My God, My God, Why hast thou forsaken me?” (Matt. 27:46; Psa. 22:1)
He was completely alone in this suffering. In Psalm 22, the Lord contrasts Himself with others who trusted, and were delivered. But He, though He trusted perfectly, was forsaken in His hour of greatest need. His agony of soul is described: "Save me from the lion's mouth!" This kind of suffering works expiation; atonement.
Christ's sufferings from man's hands do not make up any part of His atoning sufferings. It is true that the sufferings from man culminated at the very same point where God's wrath is also found (the cross), but:
"...all close and reach their limit here; all stop totally and wholly in their nature short of the wrath and forsaking of God."
Why does scripture spend so much time on Christ's sufferings from the hands of man? Perhaps because we can relate to them? They show us how truly Jesus was fully a man. Also, it helps us in our minds transition to the atoning sufferings.
Taking away the Sin of the World. The work of the cross laid the foundation for Christ to not only reconcile lost souls, but also to redeem the fallen creation and cleanse the universe of sin. This is contemplated in the expression of John the Baptist, who said when he saw Jesus coming to him, "Behold the Lamb of God, who takes away the sin of the world" (John 1:29). The sin of the 'cosmos' (or, universe) has not been taken away yet... but one day it will. That work is still future. And the foundation for that cleansing, and for the creation of a new heavens and earth, was laid in the atoning sufferings. This is spoken of in 1 John 2:2, where it says "he is the propitiation... for the whole world" (1 John 2:2). The propitiatory aspect of atonement was required to cleanse the universe of sin.
The Suffering of Death. Why was death required for atonement? Because for the weight of our sins to be fully met, death was required. "The sting of death is sin" (1 Cor. 15:56), and "the wages of sin is death" (Rom. 6:23). Therefore, it was necessary for Christ to endure "the suffering of death" (Heb. 2:9). But Christ went into death under the sentence of our sins, and rose victorious over death; therefore, the sting is gone! Death no longer holds that meaning for the Christian. Death is but the servant that brings us to Jesus.