Castoroides are passive. If you see one check the immediate area for beaver dams. Beaver dams give you wood, cementing paste, and rare mushrooms/flowers. Beaver dams offer one of the fastest cementing paste gathering rates in the game. Once you open a beaver dam all castoroides become hostile so be quick. When you grab cementing paste from the beaver dam inventory make sure to dump all the wood or excess thing you will not collect. This is important because more cementing paste will not spawn once it's taken, a new dam needs to be created. By dumping all items the beaver dam is destroyed and a new one will be created later. Wild beavers are not worth killing. They offer little pelt if any and leave a mean bite.
The way to tame these guys is to run up to one of their dams and then open it and then immediately close it (you don’t have to take anything from it, opening the dam will immediately aggravate all and any nearby beavers). Once this step has been done, you must bola the beaver (assuming only one tries to fight). I actually made a hearty mistake and bolaed the first one that came whereas I should’ve killed the second first (I was making a video, the second one got killed). Once the beaver is bolaed and separated from its mates, go behind it where it can’t hit you and hit it with a bat until you knock it out, but before doing any of these either kill jellyfish for bio-toxin for torpor (the beaver’s torpor will drain quickly) or farm a bunch of narcoberries in preparation. These guys are herbivores so you should also farm other berries besides narcoberries, or gather from the nearby forests. Keep in mind that beavers EXTREMELY slow eaters when knocked out, so patience is your weapon here.