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There's no direct way of doing this, but here's an idea. Create a label in Gmail called "[From date] to [To date]" with the date range that you want to clear out. Do a simple search in Gmail and find all the emails within that date range. Apply that label to all the search results. Go to Gmail's IMAP settings and make sure that label is set to show on IMAP.
Then use an IMAP client to log into Gmail. Go to the folder for that label, select all the emails in there, and drag and drop them into a local folder on your email client.
Go back to Gmail, find all the email with that label. Delete them all (Select All => Select all mail with this label => Delete) from Gmail.
That should achieve the end you want.
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