How can the prohibition on murder be reconciled with capital punishment in the Torah, i.e., mitath beth din? I understand that the death penalty was effectively abolished by the Sanhedrin in 30 CE. However, before that change was made, how could the administration of capital punishment be reconciled with the prohibition against murder? Was the argument that execution of a guilty person was not considered "murder"?
Judicial execution is not the same as murder. The same torah that says "do not murder" also calls for the death penalty for certain transgressions, so there must be a difference.
Tractate Sanhedrin discusses capital punishment in a fair bit of detail. There are strict rules, but nonetheless a death sentence is possible and does not violate lo tirtzach.