There is no minimum cut off. This thinking is completely wrong.
The mentality that immigration is a one way relationship is wrong. Canada and Canadians really really needs immigrants to come and live there. Because their population is aging, government needs tax payers to sustain its expenses and provide services to Canadians, especially retiring Canadians.
However, they of course want to have controlled and steady inflow of people because they cannot overnight construct new homes, roads and other infrastructure to accommodate more than certain number of people. So they have a limit in terms of number of people who can come in. Next thing is the ensure people who are coming in are paying as much tax as possible. And for that they would want people who are most likely to succeed in their career in Canada. They don't know anyone personally and they cannot discriminate so they have created a fair and equal system for everyone.
Immigration is for filling a gap. As long as there is a gap (which is infinite), there will be new ITAs. Express Entry is an open system, that is anyone can apply to be part of the pool without any direct costs but only top candidates will go though, if top candidates have score above 450 then that's cut-off score. If top candidates in pool have score of 350 then that would be the cut-off score. CIC doesn't have cut-off score in mind.
One change that is likely coming in EE soon IMHO is that CIC might start issuing ITAs to tops scorers in specific occupations. Just like the draws they did for CEC. So cut-off score might go much lower for high in demand occupations but stay much higher for others.
However, those with scores below 400 should be practical to stop dreaming about getting an ITA until cut-off score reaches below 420! Until then it's best to spend time on meaningful things.
Good luck!