Mythbusters (lost unaired segments of Discovery Channel science entertainment series; 2006-2015)
Mythbusters is a popular science entertainment TV program, hosted by veteran special effects artists Jamie Hyneman & Adam Savage, that puts various modern myths, storytelling tropes and urban legends to rigorous scientific test. Adam & Jamie then use their results to determine if the myths are in reality "plausible" or "busted". Over more than a decade, this has resulted in some startling and surprising television... but in only two cases was it so startling that the footage never made it to air.
In the 2006 Mythbusters episode "Steam Cannon," among the myths being tested is "there's more nutrition in the cardboard box than the cereal." The resulting segment, as aired, features Adam & Jamie exploring various means of determining the nutritional content of cardboard. While mostly unremarkable, it comes across as a bit vague and disorganized in comparison to the show's usual meticulously planned investigations.
In a Q&A some years later (and several times since) Adam explained that this was because the original plan for testing this myth had gone so horrifically awry that it was unusable. According to his account, the experiment involved lab mice placed in three groups - one eating normal mouse food, another sugary cereal, and the last cardboard box pellets. After several days' filming the crew had noticed on the Friday afternoon that the cardboard-eating mice were acting strangely; on resuming the following Monday morning, they discovered that one of the "cardboard mice" had eaten the other two mice in its cage. All that remained of each victim was, in Adam's words, "...a head, and a tail, and nothing but a ribcage in-between."
The show's producers at the Discovery Channel refused to allow the debacle to be part of the episode. In the segment as aired, Jamie only very obliquely alludes to not wanting to actually eat the cardboard out of concerns over toxicity. However Adam claims that in the initial footage both he and Jamie had tried to play the ruined experiment off as gruesomely hilarious, holding up the 'very fat' cannibal mouse (which they had dubbed 'Killer') and joking along the lines of 'when mice attack!'
"Easily Available Explosive"
At the 2016 Silicon Valley ComicCon Adam told the story of another unaired segment, albeit this one was said to have been scrapped entirely so that supporting evidence is shakier. Apparently, some time during the 'Build Team' (Grant Imahara, Tori Belleci, and Kari Byron) era from 2006-2015, the trio set out to test a myth about the explosive capability of "a commonly available material". According to Adam, their mindset was "[this thing] is supposedly very explosive, let's see if it is true. If it is we will censor out details so people can't make it at home, but it likely isn't, so we'll be telling people not to waste their time doing it."
Thus everyone was shocked and horrified when the results turned out to be so spectacularly explosive and dangerous that, instead of merely censoring the instructions, they destroyed all footage and agreed never to talk about the experiment again - except when Adam reported their findings to the Defense Advanced Research Projects Agency. 
Adam had made a rough cut of the "cannibal mouse" footage by the time the decision was taken to pull it, and in the Q&A he admits to showing it at "Northern Michigan Tech" (likely referring to either Northern Michigan University or Michigan Tech University). When Discovery found out, however, they forbade him from showing it ever again.
Mythbusters ceased first-run production as of 2016 - and despite his claims that the producers insisted he destroy it, it's plausible that Adam may still have a personal copy of the footage. But due to the graphic animal violence it remains very unlikely it will ever resurface publicly. The Discovery Channel has always done their best to keep a family-friendly image and strictly avoid any hint of animal harm (never testing the myth of "drying a dog in a microwave" in any form, for instance).
Meanwhile, the "easily available explosive" footage is evidently likewise lost, although if Adam's tale is accurate presumably some record of the results survived to be presented to DARPA. Again, however, whatever materials may still be held privately there is strong incentive never to release them publicly.
- Fifth Gear Europe (partially found Discovery Channel Europe motoring series; 2009)
- Land of Lost Monsters (found Discovery Channel special; 2003)
- PitchMen (found Discovery Channel docudrama series; 2009-2011)
- Top Gear (partially found Discovery Channel adaptation of BBC Two motoring series; 2005)
- Darcy's Wild Life (found Family Channel/Discovery Kids teen sitcom; 2004-2006)
- Kenny the Shark (partially found live-action Discovery Kids special; 2000)
- Kenny the Shark (partially lost unaired pilots of Discovery Kids animated series; 2001)
- The Paz Show (partially lost TLC/Discovery Kids animated short series; 2003-2006)
- My Little Pony: Friendship Is Magic "Spike at your Service" (found early drafts of Hub Network animated fantasy series episode; 2012)
- Family Game Night (found Hub Network game show; 2010-2014)
- The Game of Life (partially lost Hub Network game show; 2011-2012)
- 2010 Adam Savage Q&A on the Cannibal Mouse segment. Retrieved 17 Jan '23
- 2016 Adam Savage Silicon Valley Comic Con Q&A About the Explosive Retrieved 9 May '23