First off, the photo you're trying to delete must have been uploaded by the app that's trying to delete it. This is mentioned in the Facebook Documentation: A photo can only be removed by the same app that published it.
You'll need a valid Page Access Token to delete the photo too. You can get this my adding the manage_pages
permission and calling /me/accounts
to get the list of access tokens, finding the one for the correct page).
Finally, calling: https://graph.facebook.com/{PHOTO_ID}?access_token={PAGE_ACCESS_TOKEN}&method=DELETE
will delete the photo if the app has permission, otherwise you'll receive a error like:
{
"error": {
"message": "(#200) Permissions error",
"type": "OAuthException",
"code": 200
}
}