Using Time Machine with an Airport Extreme AirDisk
Q3. How do I delete backups?
If that sparse bundle is very large, and OSX says it will take many hours to delete it, there is a faster, but more tedious, way:
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•Cancel the deletion.
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•Control-click (right-click) the sparse bundle in the Finder and select Show Package Contents.
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•Open the bands folder (it may take a while to show the contents).
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•Select a large number of bands (up to about 8000 at a time), and delete them.
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•When they’re all deleted, delete the sparse bundle.
It depends on exactly what you want to do, and why.
Under normal circumstances, you shouldn't have to delete anything. Time Machine automatically "thins" (deletes) backups every time it does a new backup, on the following schedule:
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•"Hourly" backups after 24 hours (except the first of the day, which is a "Daily" backup).
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•"Daily" backups after a month (except the first of each week, which is a "Weekly" backup.)
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•"Weekly" backups are kept until Time Machine needs the space for new backups; then one or more of the oldest weeklies will be deleted as necessary to make room for new ones.
However, Time Machine will never delete the backup copy of anything that was on the disk being backed-up at the time of any remaining backup. So all that's actually deleted are copies of items whose originals were changed or deleted before the next remaining backup.
But if you do want or need to delete backups, here's how:
(If want to delete much, it's faster to disconnect the USB drive from your Airport Extreme and connect it directly to your Mac.)
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•To delete individual backups, or all backups of selected item(s), see Time Machine FAQ #12.
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•To delete everything on the USB drive, or one partition on it, see #1 or #2 in Using Disk Utility.
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•To delete all the backups for one Mac, without disturbing anything else, delete the sparse bundle via the Finder. If it's quite large, and the deletion is very slow, see the blue box below.
Time Machine can back up to a USB drive 
connected to the new, tall Airport Extreme "ac" models (6th generation) introduced in June, 2013.
But it's not reliable and not supported by Apple on the older, flat models. They have different hardware. If there's trouble with it, you won't get much, if any, help from Apple. If you decide to take the risk, you'd be well advised to have other backups; don't depend on these 100%. See Time Machine FAQ #2 for supported Time Machine destinations.