Organ transplants and donations have recently evolved, which means that 2,000 years back, this concept would have been unknown. To make it relatively clear to you, the Bible does not specifically mention organ donation or organ transplantation, but we can certainly draw inspiration from Christ who sacrificed himself on the cross.
As followers of Christ, we are called to serve not just the church, but our brethren in need. Which just goes to say, we can be good Samaritans by donating our organs to someone in dire need of one. Here's evidence from the Bible to support organ transplants.
One of the greatest commandments given to us is to love one another just as Jesus loved us. As Christians, we are called to do unto others as we would like to be done unto ourselves. As a follower of Christ, we should never forget that an act of kindness shown to the least of God's people is actually an act done to serve God. In Matthew 25:40, we hear Christ saying, "... 'Truly, I say to you, as you did it to one of the least of these my brothers, you did it to me'." In these terms, donating an organ would definitely be an act of selfless sacrifice for another. So to say, God forbid if someday we are on the receiving end, there will be someone who will be known as our helper in distress.
Luke 10:25-37 deals with the parable of the Good Samaritan and also tells us how to recognize such an individual. If you are still wondering what this passage has to do with organ donation, read between the lines. An individual who helps another without ever thinking about his gains or loss is a Good Samaritan. In other words, anyone who shows mercy and compassion to another fellow being is a Good Samaritan. Giving selflessly entails not thinking about benefits, which again points to not hesitate about donating your organs. Besides, 1 John 3:17 says, But if anyone has the world's goods and sees his brother in need, yet closes his heart against him, how does God's love abide in him?
The ash we are anointed with on Ash Wednesday is not a grim reminder that we shall all perish someday, but on the contrary, is a sign to rise in salvation. Still confused, if you should sign up for an organ donation? Well, according to Genesis 3:19, By the sweat of your face you shall eat bread, till you return to the ground, for out of it you were taken; for you are dust, and to dust you shall return. To say the least, at the time of your death, you do not take any of the earthly inheritance, not even the body you were born in; instead, you are raised in spirit and taken to your heavenly abode. This means that you can rest assured that God won't look into your human body to see if its parts are missing, but into your soul, which will reveal every answer that God seeks.
As Christians, we should always remember that when we give selflessly to another, we reap the benefits in heaven. While the earthly body shall pass from us, our spirits shall rejoice for every good deed done on earth. For God has promised each of us with a heart of love that replaces our heart of stone, each time we perform a good deed.