giant vampire tarsiers.

Bear with me.
The most commonly described form of chupacabra seems to be a mid-sized biped that leaps like a kangaroo on long hind legs, has large eyes and sharp fangs. It has small forelimbs that it uses to grasp prey.
This, to me, seems indicative of some kind of primate, but not an ape, or even a monkey like a macaque. I’m thinking a large, ground-dwelling tarsiiform.
Tarsiiforms (the group of lemurs that includes the tarsiers) are small insectivorous lemurs that travel by leaping from tree to tree. They are the only entirely carnivorous primates, have big bug eyes and show up in the fossil records on Africa, Asia, Europe, and North America, the focal point of all chupacabra sightings.
So let’s say a lineage of tarsiiforms ends up in the Americas. Migrating to the dry regions of Central America , these critters come to the ground. They adapt their springy hind legs into jumping organs like those of a kangaroo. They grow in size because they can; they no longer need to remain small. Over time they take to hunting larger prey. Since water is scarce in this environment, they start drinking the blood of their prey. Their fur becomes thinner, perhaps even vanishes, in order to keep cool, hence their mangy appearance.
After a few million years, we have a textbook chupacabra; a bipedal bloodsucker that leaps like a kangaroo and bites like a vampire. They would have a slow metabolism and engage in regular feeding frenzies to compensate for the low-calorie diet, (this concurs with the nature of livestock kills) and be near-hairless.
As to anatomy? Just think giant bald tarsier with kangaroo legs and you’re on the right track.