There are multiple ways of expressing the sentence.
The first is the long version:
Data uploaded to X and data downloaded from X.
When using a parallel construction, you can't omit a part that would result in an incorrect expansion. So, for instance, neither of these work:
✘ Data uploaded and downloaded to X.
✘ Data uploaded and downloaded from X.
Although the second sounds slightly better than the first, because from works directly after downloaded and to doesn't, they both end up with one of the verbs using an incorrect preposition.
So, to shorten it, you can't omit either of the prepositions.
Both of these will work:
Data uploaded to and downloaded from X.
Data uploaded and downloaded to and from X.
It's also possible to shorten it even further in one of the following fashions:
Data transferred to and from X.
Data transferred between X and Y.
Which version you choose is up to you.
As for the version in the question with the slashes, I would say it's grammatical—but, to me anyway, more visually confusing than any of the reworded versions that don't use slashes.