Most of you already do this step. Archive your classes to keep your Google Classroom landing page clear of old classes. 

Archiving the classes DOES NOT delete them. They are still there and you can restore them any time you want.  I recommend not deleting the classes because archiving them gets them off your landing page. Plus if you ever want to copy an old Class, you still have them available to you. 

You might not know this, but Google Classroom creates a folder in you Drive for each class you have created. 

I recommend you don't delete these. It stores all the work of you students and all the templates for assignments you created as well. 

Instead create a new folder in your Drive for the school year and then just drag and drop your folders into the year folder. 

Finally, head over to your Google Calendar. Once again Google Classroom creates a calendar for every class you create.

This can make that list of calendars quite extensive. You have a couple options to tidy up your Calendar list. 

First option is to just hide it from the list. Click the 3 dots from the list and you get the drop down, see picture above. Simply click Hide from list and you're done. The calendar is gone from your list. 

Second option is to actually delete the calendar. When you click on the 3 dots, click on Settings and sharing. Scroll all the way to the bottom and select Delete. Not sure what the benefit of deleting the calendar is, but you have the option to do so.