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.