In addition to writing values and reading them using HTTP calls, you can also clear a channel on ThingSpeak. To do this, you'll need to construct a DELETE request in the following format, as per the ThingSpeak documentation:
DELETE /channels/CHANNEL_ID/feeds?api_key=USER_API_KEY HTTP/1.1\r\n Host: api.thingspeak.com\r\n \r\n
Note that you'll need to find your CHANNEL_ID (likely a 6-digit number) and your user API key, which can be found on your ThingSpeak profile page.
Write a program that clears one of your ThingSpeak channel from your Arduino/ESP8266.
Note that the ThingSpeak Arduino library does not have a function for clearing a channel at this time, so you will need to manually make the HTTP DELETE call. If you need, refer to the "GET a Web Page" lecture to see how to make HTTP calls.