* "He was referring to her as her dog." (This is the most natural and grammatically correct way to express the idea.)
* "He called her 'her dog'." (This is a more informal way to say the same thing.)
* "He made a derogatory remark comparing her to a dog." (This is a more formal way to express the idea, emphasizing the insulting nature of the statement.)
The key is to use the correct grammar and word choices to clearly convey the meaning you intend.