I had willow branches like that and my pup pulled them up thinking they were sticks he could chew on.
I had to surround my new garden with chicken wire, it's 3 1/2' high but I recently saw him jump it...so need to go higher. Here's Wall-e.
I too need to find some more(hopefully attractive) ways to keep him out of the gardens, or until he gets older just keep my gardens in the front yard on the other side of our fence.