You can use Google Drive to get your photos and use an other software to delete duplicates.

• Go to https://www.google.com/drive/download/ and download Backup and Sync
• Go to https://drive.google.com/ and enable "Create a Google Photos folder" in the options.
• All your photos will be available in your computer under your Google Drive folder. It may take a long while to download all your photos.
• After your photos are downloaded, use a software to find your duplicate photos. There are lots of free programs that will find your exact or similar photos:
  • Good old picasa https://picasa.en.softonic.com/
  • https://www.duplicatephotocleaner.com/
  • https://www.easyduplicatefinder.com/
• The duplicate files that you delete will also be deleted from google photos.

There are some exceptions where the photos are not deleted from google photos to protect you from accidental deletes.

• If you delete a folder, the photos in that folder won't be deleted
• If you added the photos to an album, they won't be deleted
• You can read the details here: How Google Photos works with Google Drive

EDIT:
As someone suggested, this method will no longer work. As Google itself says in this link: Upcoming changes to Google Photos & Google Drive

From 10 July 2019, Google Photos and Google Drive will no longer synchronize automatically.