He would have faced a prison sentence but for mitigating circumstances.
Is it an incomplete sentence?
'Mitigate' meaning-make less severe
It might seem like an incomplete sentence if you treat but as a conjunction and for as the start of a prepositional phrase.
However, when parsing that sentence, you need to treat "but for" as a single unit:
From the webpages of The Free Dictionary:
Idiom:
but for
Were it not for; except for : We would have reached the summit but for the weather.
Therefore, the sentence you have provided in your question is both grammatical and complete.
(You may have been able to figure this out on your own but for that tricky idiom.)