The Bible does not specifically mention euthanasia, but it does address issues closely related to it. Euthanasia is known by different terms such as mercy killing, assisted suicide, etc. It is the act of assisting someone in his or her own death who is terminally ill, suffering, and in great pain. The goal of the assisted suicide is to prevent the continuation of pain.
The Bible tells us that we are not to murder (Exodus 20:13). Murder is the unlawful taking of life, and killing is the lawful taking of life. Technically speaking, if a nation said that euthanasia was legal, then on a human level it would not be murder. But as societies often legislate moral issues in contradiction to the Bible, just because a society might say that euthanasia is good does not mean that it is. We are to obey God rather than men (Acts 5:29).
We are made in the image of God (Gen. 1:26), and it is the Lord God who gives us life (Job 33:4) and who has numbered our days (Job 14:5). This means that God is the sovereign Lord who determines the day that we die. Therefore, we are not to usurp God's authority.
In the Bible...
In the book of Job, when Job is under great distress and in great pain, his wife says to him “'Do you still hold fast your integrity? Curse God and die!' 10 But he said to her, 'You speak as one of the foolish women speaks. Shall we indeed accept good from God and not accept adversity?' In all this Job did not sin with his lips,” (Job 2:9-10). Basically, Job's wife wanted him to euthanize himself to avoid the pain of his life, but Job refused to do so and in this, he did not sin.
Heb. 9:27, “And inasmuch as it is appointed for men to die once and after this comes judgment.”
The Bible tells us that it is God who appoints people to die. Essentially, assisted suicide is an attempt to deny God his sovereign right to appoint who dies when. We must be careful not to take into our own hands the right that belongs to God.
There is nothing in the Bible that tells us we must do everything we can to keep someone alive for as long as possible. So, we are not under obligation to prolong the life of someone who is suffering. If someone is terminally ill and in great pain, we should make the person as comfortable as possible during this process of dying. We should not hasten his death. Instead, we should let death take its natural course, but make every effort to comfort those who are suffering.
Finally, like so many things in the world, when a small compromise is made many injustices are eventually allowed. If euthanasia is permitted under the emotional and moral claim that it is best for the individual, what is to prevent the government from eventually stepping in and determining who else needs to be terminated? Might the definition of euthanasia be expanded to include those who are suffering from chronic depression, or just don’t like living -- or are not productive in society? We must ask that if the door to killing people in their old age is opened, can it ever be closed again?
Think about it. The beginning of life is now open to destruction in abortion, and the end of life is now being considered for destruction as well. Like a vise that closes from either end, how many of those in the middle will fall prey to the depravity of man's moral relativism and love affair with sin that always brings death?