Yes and no. This article from the Telegraph newspaper confirms that the makers mostly used CGI, practical effects (e.g. props) and stand-ins for the animal corpses. The dead bear, bison and the horse corpses were a mixture of props and CGI and the the bear skins and bison liver were sourced ethically from Nation Park animals which presumably died of natural causes (or were at the very least culled rather than being killed specifically for the film).
That being said, the fish was a real fish.
“Standing in a freezing river and eating a fish, or climbing a
mountain with a wet bear fur on my back — those were some of the most
difficult sequences for me,” said Mr. DiCaprio, who is considered a
strong contender for an Oscar nomination for his performance. “This
entire movie was something on an entirely different level. But I don’t
want this to sound like a complaint. We all knew what we were signing
up for. It was going to be in the elements, and it was going to be a