The snapshot will be locked by the clone, and until this clone is either deleted or split, it will keep this locked. Snapmirror isn't running any updates, so the primary volume won't remove the snapmirror snapshot. You can manually delete this snapshot from the primary as you won't be using snapmirror again (I image?).
If this is a one off operation (or maybe a monthly operation), would you not be better off by doing the snapmirror, then breaking it and bringing the mirrored volume online and available for use in your QA environment?
But short answer, no, the snapshots won't be deleted automatically, so you will need some form of manual intervention or your volumes will continue to grow.