Here's a whole page of quotes from Clive Barker before, during and after the making and release of Hellraiser III.
http://www.clivebarker.info/hellraiser3.html
This is maybe the most relevant quote to your question.
But I refused to put my name on it. I really don't want to be like Stephen King! While it was beautifully composed, the actors nicely framed and the images were slick, there was obviously a lot of stuff missing which rendered it incomprehensble in parts. Hickox tends to work fast - and it showed! Because it was shot back-to-back with Children Of The Corn II for economic reasons [both shared the same crew], Kuppin's penny-pinching hadn't served the special effects well either. As it didn't reflect my vision of the Hellraiser mythos, I had no desire to be associated with it in any way.