Why does a shared photo disappear from Smugmug once I delete it from the Aperture?

Aperture is syncing with the online albums. Any changes you do to the albums in Aperture will be reflected in the shared online album. See the page in Aperture's "Help":

After you set up your account information and create your first web album, creating new Flickr, Facebook, and SmugMug albums is a simple process.

You can also delete web albums in Aperture at any time.

WARNING: Deleting Flickr, Facebook, and SmugMug albums in Aperture permanently deletes the corresponding sets, albums, and galleries online, along with their contents. If you want to temporarily remove an account in Aperture, but keep the albums and photos as they are in your web account online, you can always disable your web account in Aperture. For more information, see Manage your Flickr, Facebook, and SmugMug accounts.

If I want the files removed from my computer but to remain in smugmug then what i do is break the link. To break the link you can go into smugmug and create a new gallery with a similar name. then I move all the photographs which aperture uploaded into the new gallery. That breaks the link. if you go into aperture and try to sync - aperture won't find the remote files. So if you were to delete the files now in aperture the smugmug gallery wont be impacted.

note: renaming the gallery in smugmug will not work. i suggest you try to delete one image first to see if it gets deleted from smugmug as well to confirm first that the unlinking workd.

hope this helps.

cheers.