Spoilers ahoy, if you haven’t yet cleared Act 1.
Midway through Act 1, we learn that Tyrael used to be an angel. Upon disagreeing with his fellow angelic brethren, he opted to fall to Sanctuary and aid the humans in fighting the demons that were poised to overrun it.
Tyrael appears human – so much so that Leah doesn’t believe him to be anything more than a man, until he shares his fall from heaven with her in a vision. Later in the game, he mentions that he is mortal, so presumably the gesture was not just symbolic, and he’s not angelic anymore. However, humans in the Diablo series are descendants of the Nephalem – the offspring of angels and demons.
It doesn’t seem like Tyrael’s tearing of his wings made him partially demon, so what is he exactly? Is there any precedent or explanation for this in the lore?
Tyrael is a walking, talking Deus Ex Machina.
There is no precedent or explanation in lore other than ‘Angels are powerful and they can turn one of their own into a mortal by ripping off his wings because that would be cool, OKAY?’
This is Blizzard we’re talking about. There are tons of plot holes, and very few of them make sense. The best we can hope for is a retcon at some point in a piece of fiction or an expansion that makes a ham-handed attempt to explain things, introducing seven more complications in the process.