The game storyline seemed to indicate that Axel hoped to provoke Sora by kidnapping Kairi, and if he gave way to the darkness again, he would become a Heartless again and Roxas would return. I really don't see how he could have pulled that off, and Roxas would probably have been furious with him, but supposedly this is what he was trying to do.
However, I've read some excerpts from the novels which said that Axel wasn't exactly trying to kidnap Kairi; he knew that Namine wanted to meet her and he was trying to reunite them. Later Riku asks him if he's going to try turning Sora into a Heartless, and he answers, "Maybe." This makes me think the whole Sora-Heartless idea was merely a backup plan, and he wasn't really sure what he wanted to do.
So Saix's words might have meant one of two things:
1. He sincerely believed that Axel wanted to hurt Sora and warned him in order to keep him alive (and gather hearts of course!).
2. He was lying to turn Sora against Axel and basically keep him isolated from a potentially important ally. (like Marluxia did in Castle Oblivion) If Axel had decided to stick with Sora and help him out, they could have caused a lot of damage to the Organization much earlier.