I would say it's not obviously grammatically incorrect, but the structure of the sentence doesn't clearly communicate what it means. The first part is okay. The problem starts at OF. "the coffin of how biased he is" doesn't really make sense, at least to me. Also, does "with that statement" apply to Paul, or HE?

The interviewer nailed the coffin shut with that last statement, Paul was no longer interested in working for a baised employer. Paul nailed the coffin shut on the interview and respectfully ended the conversation. The last comment was intolerable and biased. When I use metaphors and similes. I try to illustrate a picture. It's more of an artistic way of speaking and if you fail to paint a vision in the listeners head. It just sounds odd and takes the focus away from the original point. Here's two examples of both Paul and the interviewer nailing the coffin shut. Either party could have killed the interview. It depends on the picture you want to draw. Hope that helps

‘Putting the final nail in the coffin’ refers to ending something or killing something. It isn’t a good fit for your example. Here you are suspicious that Paul is biased and then he says something which confirms your suspicion. Nothing is being ended. You could flip it around and talk about how your hope that Paul was unbiased had ended. But in general forcing the use of expressions of this kind won’t be natural. To be natural, it would have to fit the situation exactly. Just learn to say things precisely using normal vocabulary. That’s always possible but not always easy, even for native speakers.