You can set a date on the sheet by adding a date in the “General” section when editing a sheet (below the sheet description field). Alternatively, if you are using the Pro version, you can set dates on each task by selecting the “Use Task Dates” checkbox which allows you to set a date on each task. Once the date has passed the sheet or task will become deactivated and not allow further signups.
If you have any other questions, just let me know!