The immortality of the Mo Clan is unparalleled. They can never die under anyone's circumstances, and the only one who can kill them is the person they love. Still, this weakness was cleared after the couple got the imprint of marriage to remove all weaknesses in their constitutions. This includes the Mo Clan's weakness of dying under the hands of his beloved. This immortality isn't like the one he shared with his husband before, where he experiences death after death and then gets revived.
With Hei Anjing giving him immortality, Ye Xiajie no longer possessed the ability to die. He is immortal unless he wishes to die. Though this immortality physique is immature for newly born Mo descendants, a mature god is completely different. At least their own lives and deaths are under their control. It is like when Snow from a thousand years ago chooses to destroy himself, it's the choice of the owner of this immortality that made him accept death. All he needed to do was control it.