Assuming a key akin to "deadline", you could use or adapt the following:
WHERE dateformat(deadline, "yyyy-MM-dd") <= dateformat(date(today), "yyyy-MM-dd")
Or work with note creation date:
WHERE dateformat(file.date, "yyyy-MM-dd") <= dateformat(date(today), "yyyy-MM-dd")
Instead of "today" use "this.file.name" when working with daily notes as in your case.
To have the list be divided into completed and unfinished, skip the "!completed" and instead use:
SORT completed
Add DESC to reverse order.
Another option would be to have two separate dataview queries. One for completed and one for unfinished tasks.