Animals are raped, tortured, and killed throughout each series. At least two dogs meet this fate as well as a vulture and a dolphin (I've only read a few issues skipping around).
Crossed is extremely gratuitous with its gore and holds back no punches, nearly everything described as a content warning is shown clearly in detail on panel, with very minimal subtlety
I'm not 100% sure a Cat isn't hurt, but I've read enough that I can surmise that No, a cat isn't hurt in most of the comics, there is a scene with a jagaur/leopard(?) But it isn't hurt, hell it even kills many of the Crossed, it isn't infected though.
Obviously elsewhere aswell(some in wideshots including of already dead corpses) but in Family Matters at the sanctuary a man is shown being hanged for a crime, aswell as in one of the badlands shorts where another man is hanged