The quoted excerpt from Isaiah 53 above clearly occupies substitutionary language. This passage foretold Christ bearing the sins of mankind upon Himself. He was offered up in the same manner as an unblemished lamb for our sins (1 Peter 1:18-19). His innocent blood was shed for both the just and the unjust (1 Peter 3:18). Our sins are forgiven and removed by His wounds (1 Peter 2:24). The previously referenced passages from the New Testament are based on the vicarious nature of the atonement sacrifices performed under the Mosaic Law:
"When he finishes atoning for the holy place and the tent of meeting and the altar, he shall offer the live goat. Then Aaron shall lay both of his hands on the head of the live goat, and confess over it all the iniquities of the sons of Israel and all their transgressions in regard to all their sins; and he shall lay them on the head of the goat and send it away into the wilderness by the hand of a man who stands in readiness. The goat shall bear on itself all their iniquities to a solitary land; and he shall release the goat in the wilderness." (Leviticus 16:20-22)
Animals paid the price for the sins of people with their very own lives. They were an innocent substitute. Though animal sacrifices served as a temporary covering for sin, the Levitical sacrificial system pointed to the perfect, once for all sacrifice of Jesus Christ (Hebrews 10:1-2). Richard L. Mayhue provides this helpful synopsis of Isaiah 53:
"1. v. 4 - "our griefs He...bore" 2. v. 4 - "our sorrows He carried" 3. v. 5 - "He was pierced... for our transgressions" 4. v. 5 - "He was crushed for our iniquities" 5. v.5 - "by His scourging we are healed" 6. v. 6 - "caused the iniquity of us all to fall on Him" 7. v. 8 - "He was cut off...for the transgression of my people" 8. v. 11 - "He will bear their iniquities" 9. v. 12 - "He Himself bore the sin of many"
The New English Translation has this footnote on Isaiah 53:5:
"tn The preposition מִן (min) has a causal sense (translated “because of”) here and in the following clause. tn Heb “the punishment of our peace [was] on him.” שָׁלוֹם (shalom, “peace”) is here a genitive of result, i.e., “punishment that resulted in our peace.”sn Continuing to utilize the imagery of physical illness, the group acknowledges that the servant’s willingness to carry their illnesses (v. 4) resulted in their being healed. Healing is a metaphor for forgiveness here."
The New English Translation has this footnote on Isaiah 53:11:
"tn Heb “he will acquit, a righteous one, my servant, many.” צַדִּיק (tsadiq) may refer to the servant, but more likely it is dittographic (note the preceding verb יַצְדִּיק, yatsdiq). The precise meaning of the verb (the Hiphil of צָדַק, tsadaq) is debated. Elsewhere the Hiphil is used at least six times in the sense of “make righteous” in a legal sense, i.e., “pronounce innocent, acquit” (see Exod 23:7; Deut 25:1; 1 Kgs 8:32 = 2 Chr 6:23; Prov 17:15; Isa 5:23). It can also mean “render justice” (as a royal function, see 2 Sam 15:4; Ps 82:3), “concede” (Job 27:5), “vindicate” (Isa 50:8), and “lead to righteousness” (by teaching and example, Dan 12:3). The preceding context and the next line suggest a legal sense here. Because of his willingness to carry the people’s sins, the servant is able to “acquit” them."
The following noteworthy excerpt was taken from a study by William D. Barrick, Professor of Old Testament:
"The Septuagint (LXX) evidences a pre-Christian Jewish understanding of atonement (especially in the use of the Hebrew words for atonement, 19 [kipper) and 19 [koper]) as propitiation since it employs é u dokopci (exilaskonal) 83 times for translating kipper." Summing up a detailed analysis, Morris deduces that the basic meanings of kipper and ĆELA.COkouci involve the thought of the offering of a ransom which turns away the divine wrath from the sinner." In addition to ransom and divine wrath, kipper "denotes a substitutionary process... so plain as to need no comment in the cases where life is substituted for life. Since the OT reveals the reality of divine wrath, it cannot be ignored or explained away as impersonal wrath, mild displeasure, mere irritation, or capricious passion. In nearly 600 OT texts more than 20 different Hebrew words provide a rich wrath vocabulary. Divine righteousness, holiness, and justice require divine retribution. Without divine retribution, divine mercy becomes nothing more than a vestigial appendage without function or purpose."
It might also be interesting to point out that Jewish commentators in centuries past had recognized Isaiah 53 as being a Messianic prophecy and also the substitutionary language contained therein. Jewish scholar Herz Homberg gave this commentary in his exposition of the entire Old Testament called Koren:
"The fact is that it refers to the King Messiah, who will come in the latter days, when it will be the Lord’s good pleasure to redeem Israel from among the different nations of the earth…and even the Israelites themselves will only regard him as ‘one of the vain fellows’, believing none of the announcements which will be made by him in God’s name, but being contumacious against him, and averring that all the reproaches and persecutions which fall to his lot are sent from heaven, for that he is ‘smitten of God’ for his own sin. The fact is, that it refers to the King Messiah, who will come in the latter days, when it will be the Lord’s good pleasure to redeem Israel from among the different nations of the earth…..Whatever he underwent was in consequence of their own transgression, the Lord having chosen him to be a trespass-offering, like the scape-goat which bore all the iniquities of the house of Israel."