How to paste images from clipboard in Safari
This is known issue with the current release of Safari. 

But pasting images from the clipboard is now working properly in the Safari Technology Preview which means the fix should be coming to the public release version of Safari shortly. 

FYI, You can go ahead and use the tech preview version alongside your regular Safari install without disrupting anything.

EDIT: Safari 10.1 was released today and fixes this issue.

EDIT #2: It seems to only work with some source applications but not others. For example, I can select and copy sections of web pages w/images and paste them into Gmail no problem (Safari to Safari). I can also copy text+images from Evernote to Gmail. But... the same doesn't seem to work when TextEdit or Notes is the source.

Relevant bug report