If a Christian chooses to show compassion to a murderer, they are well within their rights to do so. There are many other options than murdering murderers.
There is a lady in our city whose daughter was abducted, raped and then murdered by a man who took her daughter from a shopping centre. I can well understand that lady wanting to see the death penalty applied. However she has become a Born Again Christian and actually Forgiven this person. God has certainley worked a miracle here. If you want somebody killed who has hurt you deeply, have you really forgiven that person, We all are well aware of how hard something like this would be to even comprehend, and in the same position it would be likely that I would want revenge also, such is the carnal nature of man.
A point has been brought up that there are many people murdered by government officials that are innocent of any crime. How many of these are Christians, being given capital punishment for things they are innocent of. there guilt being that they choose to accept Jesus Christ as their Lord and Saviour.
No-one that knows God intimatley and has lost the "Hard Heartedness of Men" that Jesus spoke of could ever murder. Even if the government told them to do it.
King David Murdered an Egyptian and did not recieve the death penalty as described in the Old Testament, either did Cain. There is always room for a compassionate heart. Slavery is spoken of much in the bible, Yet the compassionate hearted know that selling somebody into dlavery is an awful thing to do, yet if we applied the scripture you could do it. Like Slavery the death Penalty should be done away with, in favour of a life term inprisionment.
The Compassion shown in God by sending his Son Jesus Christ to die for our Sins suggests Jesus was the Last sacrifice. This Compassionate God who we know is what sets us apart from Islam. Who certainley do apply the death penalty.