If we jump in at Paul, we are many thousands of years late in discerning a biblical teaching on capital punishment. Gen. 9:6 is where we must begin.
The Bible presents a unified teaching acrooss both Testaments about a govenrment's right and responsibility to execute capitl punishment.
Christ was distinguishing a civil matter from personal retribution. This is in line with the Pharisees misinterpretation of the civil injunction of, "an eye for an eye." Christ also had to correct their changing of that into personal retribution.
Both Testaments teach a difference between personal conduct and responsibilities committed into the hand of civil government.
I will agree that there is a distinction between the church and the civil government in many matters. For example, the civil government must be in place to maintain the peace.
However, where is the line between the civil government and their handling of civil punishment and where Christian living and biblical guideance come into play.
Do you have additional material that describes or amplifies that the Pharisees were indeed practicing personal retribution rather than carrying out the law as given to them?