First of all, it is to be made clear that the entire concept of someone dying for our sins is in utter contradiction with the Islamic view of the nature of man and God. In Islam, every individual is responsible for his/her own salvation. Everyone, male or female, can directly approach God without any intermediary of a prophet, saint or priest.
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states: It seems to me that you are coming from a Christian background. In order for you to be able to understand the Islamic position, it is important to be clear about certain points.

First, Islam, unlike Christianity, does not teach a concept of “original sin”. Adam’s sin was his and his alone; and, according to the Qur’an (for the Qur’anic narration of the story of Adam and Eve, see: the Qur’an: 2: 30-39; 7: 19-25; 17: 61; 18: 50; 20: 116-122, etc.), God forgave both Adam and Eve when they turned to God in repentance; accordingly they were once again restored to divine mercy. Hence, there is no concept of Adam passing on to his progeny an original sin, and therefore no need for stipulating a redeemer for such sins.
Second, as there is no original sin, every one is born into a state of fitrah, a state of natural innocence; sin is acquired later by our own conscious and willful actions. The Prophet (peace and blessings be upon him) said, “Every child is born into a state of fitrah (natural state of innocence.)”
Third, Islam teaches that God is All-Compassionate and All-Merciful; He is not bound by the rule of a blood sacrifice in order to forgive His servants. To assume that God can forgive only by accepting a blood sacrifice and therefore to state that Jesus or Muhammad died for our sins is not acceptable in Islam. Allah says: (O My servants who have wronged against their souls! Do not despair of Allah’s mercy! For Allah forgives all sins; for He is indeed Forgiving, Compassionate. Turn to your Lord repentant, and submit to Him before the torment overtakes you when you shall not be helped.) (Az-Zumar 39: 53-54)
Fourth, Islam teaches that every individual is responsible for his/her own salvation. Not Abraham, or Moses, or Jesus, or Muhammad can save us; they are only capable of saving themselves through God’s grace. In the words of the Qur’an: (Whoever commits a sin commits it only against himself. Allah is Knowing, Wise.) (An-Nisa’ 4: 111); (Allah does not charge a soul with more than it can bear. It gets every good that it earns, and it suffers every ill that it earns.) (Al-Baqarah 2: 286); (Each soul earns only on its own account, nor does any laden (soul) bear another’s load.) (Al-An`am 6: 164) (Whosoever goeth right, it is only for (the good of) his own soul that he goeth right, and whosoever erreth, erreth only to its hurt. No laden soul can bear another’s load.) (Al-Israa‘ 17: 15)
Fifth, everyone, male or female, can directly approach God without any intermediary of a prophet, saint or priest. God is closer to us than our own jugular veins. Almighty Allah says in the Qur’an: (We verily created man and We know what his soul whispereth to him, and We are nearer to him than his jugular vein.) (Qaf 50: 16) (When My servants ask you about Me, tell them I am nigh, ready to answer the prayer of the suppliant when he prays to Me; therefore let them respond to Me and believe in Me, that they may walk in the right way.) (Al-Baqarah: 186)
So, the entire concept of someone dying for our sins is inimical to the Islamic world-view or understanding of the natures of man and God. Islam beckons us all to respond to God’s message and receive His grace and salvation through faith, good works and leading a responsible moral and ethical life.