The Rival AI in stage 3 just keep buying stock of my company.
He went into deep red ,but he keep buying more.
He got like -1,000k already but that doesn't keep him off of my stock.
Is this a bug??

That sounds like he could be Buying on Margin, which is legit. The more of your stock he has, and the higher its price, the more credit his stockbroker will give him. Look at his Purchasing Power number.

So what I can do is to lower the profit I make in my company to destroy his purchasing power and force him to sell my stock?

Yes, if that is what you want. I just play to the mission objectives. If personal wealth is one of them, I'll be buying on margin myself.

Do check the economy though. If it is in a depression, then the only way it can go is up, which could get him out of the hole. Whereas if the economy is booming, then a slow-down will hurt the stock price.