A Biblical answer to...

why we do not practice capital punishment for murder, rape, being a homosexual or any other Mosaic offense.

In one word, Pentecost.

Do not think that I have come to abolish the law or the prophets. I have not come to abolish these things but to fulfill them. Matthew 5:17

The sins resulting in death remain sins, but blood sacrifices ended at Pentecost, the law was fulfilled. The crucifixion (Nisan 14 30C.E.) first fulfilled the need for animal sacrifices and exposed the Holiest of Holies to all men. (Mark 15:38, Luke 23:45, Matthew 27:51) Then 52 days later, 49 days (7 days x 7 weeks) after the resurrection (Nisan 17 C.E.), came Pentecost (Sivan 6 30 C.E.) (Acts 2).

By sending us the Holy Spirit, God fulfilled his need for human blood over capital crimes. His new remedy is to redeem the person and then fill the person with his Holy Spirit. This is further demonstrated, dare I even say punctuated, by the fact that he called one of the most notorious serial killers of that era to not only be his mouth piece to that generation, but every generation to come through authoring most of what we now call the New Testament.