From what I know about Zapier it works on timed intervals. You can have a script run on time intervals just before the time Zapier inputs information and delete the old info.
Another approach would probably be to have a intermediary sheet.(Lets call this sheet, "sheet1". The final sheet can be called "sheet2". When Zapier writes data to sheet1 it can trigger the onChanged event. Take the information in sheet2 delete everything, then post the new data to sheet 2.
Finally, Zapier supports webhooks. You can publish your script as a web app and have it do a get or post to the app which runs the delete function. To give it time you can use the delay that Zapier provides.
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