What do they someone who catches Beavers?

There isn't a specific job title for someone who catches beavers. Here's why:

* Beavers aren't typically caught. They are often trapped and relocated if they're causing problems, but not for any other reason.

* Trapping is often done by wildlife professionals. These professionals might be wildlife biologists, game wardens, or other professionals with the training and permits to trap animals.

* Other people might trap beavers for fur. In some areas, beavers are still trapped for their fur, but this is regulated and often requires a license.

So, while there isn't a single word for someone who catches beavers, you could say:

* Trapper

* Wildlife Biologist

* Game Warden

* Fur Trapper

It's important to note that catching beavers is often a necessary task to manage their population and prevent damage to property.