This sounds like Scar Night, the first book of Alan Campbell's Deepgate Codex trilogy.
The angel is called Carnival and we first encounter the scarred angel in the Prologue:
The angel stepped out into the lane, small and lithe and dressed in ancient leathers mottled with mould. Her wings shimmered darkly, like smoke dragged behind her. Her face was a scrawl of scars: more scars than could have been caused by the current battle with the Spine, more scars than a thousand battles could have caused. Blood spattered her similarly scarred arms and hands, and her eyes were the colour of storm clouds. She wore flowers and ribbons in her lank, tangled hair. She had tried to make herself look pretty.
I don't think the book explicitly shows Carnival self harming, but one of the characters, Dill, says:
He remembered Carnival. How much had she been shaped by brutal truths? Yet Carnival had no illusions about who she was or who she might become. Suddenly Dill understood her. Her scars were self-inflicted. She hates herself, damages herself to keep some deeper part intact. Dill’s heart clenched at the realization. Carnival’s soul wasn’t scarred and ugly: it was pure. And she guarded it fiercely.
The gorge your friend remembers is presumably the "bottomless abyss" over which the city of Deepgate is suspended. My memory of the book is that it is pretty gruesome with many exceedingly messy deaths described in loving detail.