"mutually exclusive but" is correct and usable in written English.
It can be used when two different things cannot both exist or happen at the same time, but may be possible separately. For example: "The choices of green and red are mutually exclusive but either one could be selected."
He writes on parallel paths that may seem mutually exclusive but regularly connect.
The truth is, masculinity and feminism aren't mutually exclusive but the sexist nature of lad culture suggests they are.
These prizes are not mutually exclusive, but no player in this decade has managed to earn both in one season.
I've realised that those pieces are not mutually exclusive, but that they are all dependent on each other.
The mainstay of Bhaskara's philosophy was the conviction that acts and knowledge are not mutually exclusive but, rather, mutually reinforcing.
Book lovers know quality and pleasure are not mutually exclusive, but can anything be learned about character by examining an individual's choices in reading material?
It is a truth universally acknowledged that romance and reality are mutually exclusive, but TV executives are obsessed with those two topics at the moment.
Credit where it's due to Reynolds, who sells the whole thing with smarm and charm that aren't mutually exclusive, but this is a glib, greasy idea of fun.
In the movie world, where rampant egos and personality disorders are often entirely compatible with success, these two qualities are often mutually exclusive, but not in Boyle's case.
These two goals are not mutually exclusive, but at some point the demands of the present conflict with those of the future.
Pistorius' team submitted two lines of defence, despite criticism from prosecutor Gerrie Nel, who called them "not just mutually exclusive but mutually destructive".
