All Dogs Go to Heaven; Deleted Scenes (1989)
The 1989 animated film All Dogs Go To Heaven had two very dark scenes that were cut during initial test screenings; one involving the main character Charlie being hit by the car (in the general release, the aftermath is seen), the second being a longer sequence of his nightmare of Hell. The original version also contained minor cursing, which was also edited out; the vinyl soundtrack of the song Let Me Be Surprised had Charlie saying "damn," which is clearly animated in the movie.
The original uncut version was stolen, and Goldcrest Films destroyed the remaining uncut print to avoid storage fees. Gary Goldman, the co-director and producer, was interviewed about several Don Bluth movies; when asked if there'd ever be a director's cut, he is quoted as saying,
"No. The footage that was cut, was discarded, not saved. The drawings were not archived. Goldcrest Film and Television actually refused to store the original art (drawings) and, I believe most of the cells and backgrounds were destroyed or taken to the dump in the UK. 'They said that it cost them “too much” for adequate temperature and humidity-controlled storage.' 
Because of this, it is highly unlikely that there will ever be a full, uncut version, although there have been rumors of Don Bluth owning the only uncut version in existence.