Once I put a photo in a specific album I’d like to delete it from other albums so they are clean. Is there a way to do that?

But be careful - only removing a photo from a standard album you created yourself is save and the photo will only be removed from this album. If you delete a photos from any album, that has been created automatically by the Photos.app for you, the photo will be deleted completely from your library and vanish from all albums. Never delete photos from Recents, Imports, or the Media Type albums or any predefined album - unless you want to remove it completely.

Yes. You can go to the other albums, select the photo and use the Delete key. That will delete it only from that album.

Deleting Photos from a Photos Library

1 - regardless of where you are in the library, i.e. Photos, Memories, Favorites, People, Recents, Imports, albums or smart albums, select the photo(s) you want to delete and use the key combination of Command+Delete to move the photos to the Recently Deleted smart album.    Without the Command key held down you'll be presented with a confirmation Yes/No window regarding the deletion. 

2 - click on the Recently Deleted smart albums in the sidebar.

NOTE 1: If you're using Photos 1.2 or earlier use the File  ➙ Show Recently Deleted menu option.

3 - in the Recently Deleted album you can opt to let the photo automatically delete after the 30 day waiting period is up, delete them immediately or restore them to the library.

NOTE 2: deleting a photo from an album, slideshow, book, etc., with the Delete key only deletes the photo from that item. There is no key combination that will delete a photo from a project and move it directly to the Recently Deleted smart album.

NOTE 3: deleting a photo from a Moment or Collection (the Photos window) or the All Photos window deletes ALL occurences of that photo in the library.