Phantasmal Killer; if the target succeeds the initial WIS save do they avoid all damage?

Hi @ChrisPerkinsDnD @JeremyECrawford – Phantasmal Killer; if the target succeeds the initial WIS save do they avoid all damage?

— Ellie Burr (@Elleblr) July 25, 2017

Phantasmal killer—the spell ends if you succeed on the saving throw against it. #DnD https://t.co/6aUPl9yUEc

— Jeremy Crawford (@JeremyECrawford) July 26, 2017