You can delete the responses in the form only, or in the spreadsheet only. You can delete them from both places - but these are two separate actions.
Deleting Responses From the Form
1. Click over to the responses section.
2. Click on the little three dots icon in the top right corner.
3. Choose "Delete all responses" from the menu.
4. Click "ok" when it warns you.
As it stated in the warning, this does not delete the responses from the spreadsheet if one was created.
Deleting Responses From the Spreadsheet
1. Go to the spreadsheet where your responses are.
2. Delete the entire row for each of the responses you wish to delete - you can select more than one at a time.
If you just delete the text and not the entire rows, Google Forms will still skip those rows when new responses come in. If you want to clear the responses for good, you should delete the entire row.
If you want to keep the responses but not see them, you can simply hide the rows.
You can also duplicate the sheet so that you can save old responses before you delete them from the "live" sheet.