Right now I try use colendar to create a type of reminder that let members know which events or tasks are upcoming, is there an option that let upcoming event show until some admins or moderators, or members assigned, click or select an button then desappear the event?

Yes, I am using the Upcoming Event block of calendar.

Or this can be a feedback for Calendar improvement...

Yes! You can make two different calendars: Upcoming Events and Past Events.

When you are done with an event, a moderator can just change it to "Past Events." See how there are two calendar selections here at the bottom-left:

Your default calendar can only display the Upcoming Events and you're golden!