Photos duplicated after syncing iPhone to iMac

Duplicate Sweeper is looking at the raw original and if it removes it via the Finder you'll corrupt your library. I wouldn't use it to cull out duplicates from your library. Use one of the two that I mentioned as I know they are safe.

In some cases Photos cannot recognise already imported photos as duplicates. There are two possible reasons for Photos not being able to recognise duplicates on import and showing already imported photos as new photos.

1. Format conversion: Photos cannot recognise already imported photos as imported, if the the photos are converted to a different format, when you are importing the photos. for example, if the photos are on the iPhone in the HEIC format, but you are importing them converted to JPEGs. They will appear as new photos over and over again, because the HEIC photo on the iPhone is different from the JPEG on the Mac.
2. iCloud Downloads: Photos cannot recognise a photo as already imported, if the photos is stored in iCloud and only mirrored on the iPhone. The iCloud downloads from My Photo Stream or iCloud Photos are new files, whenever the photo will be downloaded again and appear as new photos, when you sync the iPhone with the Mac.

If any of this applies, do not trust the displayed "New" photos and select the new photos to be imported manually.

Is it the same 600 or so photo each time?

Do you have iCloud Library enabled?

As for existing duplicates ysou want an app that will identify the potential duplicates, put them in an album or mark them with a keyword for easy retrieval and deletion by you. You don't want one that does the deletion itself for obvious reasons. 

I've run tests on the these two apps with the following results and found them to be safe to use:

PowerPhotos - $29.95  

PowerPhotos is the iPhoto Library Manager version for Photos and is very powerful. Although more expensive I would recommend it as it has more capabilities than the others like the capability to merge Photos libraries or copy photos, both original and edited versions, along with their metadata between libraries.

PhotoSweeper - $9.99 - Demo version available.

PhotoSweeper compares bitmaps and/or histograms so it can detect duplicate images even if they have different file sizes, file names, image sizes and capture dates.

You moved the out to the Desktop. How? Did you export them or drag them from the album to the desktop? That's not deleting them from the library. You have to select those you want to delete, hold down the ⌘ key and press the Delete key. Then go the Recently Deleted album and finished the deletion.

Also you might want to remove those 600 from your iPhone as they are the problem. Since you've got them in the library you're OK to do that.