Capital punishment in Georgia was completely abolished on the May 1, 2000 when Protocol No. 6 to the ECHR was signed. Later Georgia also adopted the Second Optional Protocol to the ICCPR. The death penalty was replaced with life imprisonment.
The last death sentence carried out in Georgia took place in 1995. It was carried out for murder; the prisoner was executed by a single shot to the back of the head.
References
Capital punishment in Georgia (country) Wikipedia(Text) CC BY-SA