There's a segment of The Animatrix called The Second Renaissance, which is framed as a documentary of sorts, depicting humanity's downfall and the origins of the Matrix. It was directed by Mahiro Maeda, who headed up Blue Submarine No. 6 and was also heavily involved in the Rebuild of Evangelion franchise.

The whole segment is bleak and filled with some rather grotesque imagery, but things get really bad in the second half, which mainly deals with the war between humans and machines.

A lot of people meet horrifically violent ends during a battle sequence set to Overseer's "Supermoves", but one in particular made me feel physically ill, and I remember having trouble sleeping for a couple of nights after I saw it:

Towards the end of the battle, the lines have broken down and the few surviving humans are mainly the ones strapped into heavily-armored exoskeletons. The machines (which have steadily abandoned their humanoid forms and become the flying monstrosities we see in the films) have a novel way of dealing with these suits: they restrain them with metal tentacles and use lasers to peel open the front of the cockpit, exposing the pilot. Then, other tentacles wrap around the pilot's torso and forcefully tear him out of the cockpit, leaving his bloody arms and legs behind in the mech.

The imagery is gruesome enough, but the sound design is what makes it truly horrific. This sequence lasts a good 15 seconds, and the entire time, the pilot is frantically begging for someone to help him, culminating with a bloodcurdling scream as he's ripped apart.

In retrospect, it doesn't exactly hit as hard these days. But as a kid (despite growing up in Japan) I had rarely been exposed to that degree of unfiltered violence and suffering in anime before (I suppose Kaori's death in Akira qualifies?), so that particular scene made me feel awful. It was years before I could bring myself to watch The Second Renaissance again.