I would argue that sanguineous is no better than sanguinary — both connote nothing more than "somehow related to blood," to the modern literary reader.
If you mean "carrying (within themselves) blood," you could coin the word sanguiferous, Latin for "blood-bearing." In the late 1800s and early 1900s, what we now call the "circulatory system" was also known as the "sanguiferous system," because it comprised the sanguiferous channels of the body (which we'd now call "blood vessels."
Another option would be to include both warm-blooded and cold-blooded animals under the general umbrella of "blooded animals." However, note that the word "blooded" already has at least two competing meanings in English: (1) having a good pedigree, (2) having combat experience. (Also note that "blooded" is not the same word as "bloodied.")
Come to think of it, your original question doesn't really explain why you're not happy with the word "animal" in the first place. I mean, approximately all animals have blood, right? So you just want to exclude insects and starfish and whatnot? You might use the phrase "the higher animals." Vice versa, do you mean to include any species from the plant kingdom, such as the bloodwood teak?
It might also help to know the context in which you intend to use this word. Is it for a scientific paper? A science-fiction story? Depending on the context, one might say that animals that "when crushed, release blood" are squishy. In vampire fiction, one might dismissively call them bloodbags.