Jesus never mentioned a word about homosexuality. BUT...Jesus did say this:
"Do not think that I have come to abolish the law and the prophets. I have come, not abolish them, but to fulfill them. Of this much I assure you: UNTIL HEAVEN AND EARTH PASS AWAY, NOT THE SMALLEST LETTER OF THE LAW, NOT THE SMALLEST PART OF A LETTER, SHALL BE DONE AWAY WITH UNTIL IT ALL COME TRUE." Matthew 5: 17ff
Killing "men who laid with other men" is a part of the "law" that Jesus insists he was not here to change.
I personally guess that the Bible is just a codification of principles of the early Hebrews...nothing more.
But...the question of what the Bible says was asked...and the Bible says that men who engage in same-sex conduct should be killed...and Jesus said he was not here to change that.