You can schedule a specific time for a survey to close in the main Survey tab --> Survey Options here:
If you want to manually close your data collection, you can do that under the Distributions tab.

Applying an expiration date to surveys does not work. I can still take the survey and so can other users. I’ve tried to re-publish it with an updated expiration date and nothing works. There should be an easier way to just close the survey. OR at least have the expiration feature work… 

Hello @midelgado,  this sounds like it may not be intended functionality. If you haven't already, I'd recommend reaching out to our Support team, to check on why your Survey Expiration setting is not functioning correctly. 

For future surveys, if you are using Qualtrics to send individual links you can set a time that the links expire. There’s an “advanced options” link in the compose email window, clicking on that allows for customizing how long the individual links are good for.