Was not because of/ but of?
How do I say this properly, when I want to say that the result was not because of x but of y?
For example: The outcome was not because of x but (of) y?
Do I use of here?
'Because of' is a compound preposition {see OALD} and is never [AFAIK] split.
A river cuts through rock not because of its power but because of its persistence.
The whole preposition may sometimes be omitted:
*/??A river cuts through rock not because of its power but its persistence.
but re-ordering may be required:
A river cuts through rock because of its persistence, not [because of] its power.
Original: The outcome was not because of x but (of) y?
I would say parallelism (parallel structures) would require you at least to keep the "of" for clarity.
Either of the below would clearly show the parallel application of "because":
...not because of x but of y
...not because of x but because of y
Without the "of", the application of the parallel application of "because" to y is not clear.