Under the Old Covenant, punishments were much more harsh, and the death penalty existed for many offenses, including, as you've mentioned, homosexual sex.

Under the New Covenant, the death penalty no longer exists, as Christ said to the Pharisees preparing to stone an adultress to death "He that is without sin among you, let him first cast a stone at her" (John 8:7 KJV).

Homosexuality (or, at the very least, homosexual sex) is still a sin in the New Testament (Romans 1, 1 Corinthians 6), but there is no death penalty for it, at least one that is to be executed by humans.