@Bisonblake nailed it well.
I understand some animals pass on due to old age/health complications (the wild horses, Jock the hippopotamus) or that it'd be for the own animal's good (ex. the drill was sent to Zoo Atlanta to live with other individuals of its kind), but I don't see what's wrong with replacing them with other individuals of the same species (ex. the wild horses, not the drill) rather than giving them the boot. Anyway, I'll list what I can remember (I'm going to say like, 2010-onwards):
-Siamese crocodile
-Bare-faced curassow
-Green-winged macaw
-Lesser Antillean iguana (?) (I have not seen this animal at the reptile house, it formerly lived in the now nonexistent South American walkthrough area a Amphibiville)
-Red-rumped agouti
-Whatever freshwater stingrays lived in Amphibiville
-Lesser kudu
-Southern pudu
-Sichuan takin (IIRC this was because they weren't getting along with their exhibit-mates and there was no other room for them)
-Collared peccary
-Przewalski's wild horse (old age)
-Their whole saltwater aquarium they used to have
-Brazilian tapir (old age I'm guessing)
-Binturong
-South American coati
-Bush dog (old age)
-Grey seal
-Harp seal (old age)
-Drill (was moved to live with the only other captive drills in the country in Zoo Atlanta)
-Lion-tailed macaque
-African wild dog (old age)
-Black-and-white ruffed lemur
-Grey crowned crane
-King brown snake (only one known in the country, and even perhaps the continent)
-American black bear
-Syrian brown bear (though I feel Polly was just a generic brown bear)
-Slender-snouted crocodile (albeit they were short-term)
-Meerkat (see slender-snouted crocodile)
-Fennec fox (see meerkat)
-Laughing kookaburra (see fennec fox)
-Emu
-Southern screamer
-Capybara
-Barn owl
-African crested porcupine (?)
-Among more birds, reptiles, etc. There's definitely more that I may have forgotten or haven't listed.
I do not know the status of the sandhill cranes and the pelicans, I saw neither on my last visit. North American elk are definitely in the process of being phased out (only one individual remaining) who I always see hanging out with the white-lipped x Bactrian stag hybrid, who also is being phased out.
Detroit I felt was at its glory when I was like a toddler, and found home videos of klipspringer, scimitar-horned oryx, whatever gazelle lived with the oryx, nilgai, bontebok, tufted deer, Asian elephants (obviously), Pondicherry vulture (phase-out), etc. I learned of the formerly-kept lar gibbons here, and the diana monkeys somewhere online.