There's nothing wrong with negotiating trophy fees in south Africa, where the outfitter typically owns the game you're shooting. If, though, this is about telling the outfitter after you've shot an animal that you won't pay the agreed trophy fee, then as everyone has said, not only is that unethical, it's likely fraudulent, and to quote
@spike.t, it's a long walk to the airport.
Having said that, if you see an animal you'd like to shoot if the price were right, and you ask and are told the trophy fee is $X, you are completely free to say that if the fee was .75$X you'd be up for it. Depending on a range of factors (is this a record book specimen, a cull, etc.) the outfitter may well say yes.
I was hunting in the Eastern Cape some years ago and we came across an old nyala bull with one horn missing. I had the price list of course, but wasn't going to shoot a non-trophy bull for a trophy fee, so I asked the PH if they were interested in taking it off and at what price. He sent a pic to the owner and spoke to him and said you can have him at half price. Done I said, and luckily, we found it again.
I'd think that 1/3$X is getting pretty low though, and unless we're talking about a cull animal, I'd be surprised it anything was sold at that price. It's not impossible in the case of culls though - a trophy impala may be $700 or so, while a cull impala could easily be $200 or even less. I've shot cull springbok at $95 each and blesbok at $100. In both cases these prices were less than 1/3 of the trophy fee.