I know for a fact that "shutting down X" is grammatical, but I am not sure if you can add the verb complement "off of Y" after it. We already have the adverb "down", so I don't think we can add a verb complement starting with another adverb "off". We can say "remove X off of Y", but I don't think the former phrase is grammatical.
For example:
They were right about shutting down the Infowars channel off of YouTube.
shutting down the Infowars channel off of YouTube.
can be:
shutting down the Infowars channel on YouTube.
OR taking down the Infowars channel from YouTube
OR taking the Inforwars channel down from YouTube
OR taking the Infowars channel off [of] YouTube OR taking the Infowars channel down off of YouTube
[off-topic: that would be great coz it ain't news]
You can take something|| off a/the wall. You can take something down|| off a/the wall.
However, shut down (close, often a business) is a phrasal verb that does not involve an imaginary surface.
take down can be a phrasal verb but here implies that YouTube is like a surface.
(I may have forgotten some variation or other.)
off of implies a surface or waves: They took him off the air.