Everything I've found so far that's either unfinished, unused or never present in the form we saw it in the trailers/gameplay demos/etc.
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"80's Filter": Removed for being system-intensive.
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Camp Omega Special Mission (E3 2013 Trailer): Unused for unknown reasons.
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P.T Active Decoy ("Lisa") (2014 TGS gameplay presentation): Presumably cut for relationship to the cancelled "Silent Hills" project.
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Missing Delivery Point Invoices (missing locations?): Removed for unknown reasons.
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"Burned/Skull Boss" Model (Kojima 2015 Launch Trailer): Unused for unknown reasons.
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Africa Burning Village Cutscene (E3 2014 trailer): Removed for unknown reasons.
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Africa Child Soldier Training Cutscene: Unused for unknown reasons.
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TGS 2014 Africa Mission (TGS 2014 gameplay presentation)
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Mission 46 Unused Dialogue (found in game files)
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"Mission 51" Unused Mission (found on CE Blu-Ray disc)
For reference,
there were some text files in Ground Zeroes that seemed to hint at content in TPP that never showed up either, including several weapons like a Machete, AK102, Mosin Nagant, SCAR and M4. A Machete Key Item can be collected in TPP, but it's a weapon for D-Walker.
I'll update the list with anything else I find in terms of cut/unused content.