<p>We have a live MySQL database that is 99% INSERTs, around 100 per second. We want to archive the data each day so that we can run queries on it without affecting the main, live database. In addition, once the archive is completed, we want to clear the live database.</p>

<p>What is the best way to do this without (if possible) locking INSERTs? We use INSERT DELAYED for the queries.</p>

Could you keep two mirrored databases around? Write to one, keep the second as an archive. Switch every, say, 24 hours (or however long you deem appropriate). Into the database that was the archive, insert all of todays activity. Then the two databases should match. Use this as the new live db. Take the archived database and do whatever you want to it. You can backup/extract/read all you want now that its not being actively written to.
Its kind of like having mirrored raid where you can take one drive offline for backup, resync it, then take the other drive out for backup.