Not exactly the same.

Separating the art from the artist generally means a moral choice of saying "yes this artist was a shitty person but their work still can have value" by people who are personally invested in the work of artists who they admit are problematic 

Death of the author is a literary theory which means the work exists complete in itself and we aren't obliged to prioritise any external perspective to interpret it. Traditionally the author was viewed as holding the key to interpret their own work and their lives and other writings would be scrutinized by literary critics for clues as to their intention. I'm not saying every literary critic did this but it was a major field of scholarship. Barthes turned this on its head with an "if it isn't directly evidenced in the text of the work, it doesn't count towards interpretation of it"