Throughout the course of Logan, it's obvious that Professor Xavier is having issues controlling his powers, and at the end of the movie, just before
X-24 kills him
he claims to "remember" what he did and expresses regret. We also hear about an incident in Westchester that killed several mutants, that sounds like Xavier may have been involved. Is Xaiver the reason there are no more mutants? Is that why he's sorry, because he knows he killed them all?
Xavier was the person who killed the 7 mutants that died in the Westchester incident. In-universe, the reporter described that event as being nearly identical to the accident at the hotel when Xavier has a seizure, so we're obviously supposed to piece together the connection. We don't know for sure who those 7 mutants were that died in Westchester, but Westchester County is where Xavier's School for Gifted Youngsters is located, and that's almost certainly not a coincidence. It seems reasonable that the incident resulted in the closing down of the school, at least, and possibly the X-Men.
However, Xavier isn't responsible for the death of all of the mutants. Xavier's seizure only killed those 7 unnamed mutants, after which he presumably went into hiding with Logan. Between the leader of the Reavers and the lead scientist from Alkali, we find out what happened to the rest. The Alkali group has been doping the food and drink supplies to suppress mutant births, and the Reavers have then been hunting down the mutants that weren't dying off on their own. Alkali's plan is to grow their own mutants through artificial insemination, and be the only ones that have such powered people.
No. Charles Xavier was sorry in that scene because he had just remembered the "Westchester incident", where one of his seizures hurt hundreds of people and even killed some. But the victims of that incident were (probably) random innocent people, not exclusively mutants, much less all the mutants in the world.
The mutants are gone because Zander Rice developed some method of preventing mutants from being born, as he explained to Wolverine himself near the very end of the movie.
