Hello and welcome.
-Which version of OS X?
-Which version of Photos?
-Where exactly are you deleting them from?
If you delete photos directly in Finder from any of your Home folders, they will stay in Photos. HOWEVER, if you are in a Finder window and viewing All My Files section, I would STRONGLY suggest NOT deleting photos from this view. All My Files can see the photos in your Photos Library directly, and if you delete one by accident, you will end up with a black image with gray circle with a black exclamation point in place of the photo.
C