Until Magit supports something like this, the behavior is easy to get
with a custom command. I have something similar to the following
command in my configuration. If you call it with a prefix argument,
it will remove the leading diff markers.
(defun km/magit-copy-region-hunk (&optional no-column)
(let ((text (buffer-substring-no-properties
(kill-new (if no-column
(replace-regexp-in-string "^[ \\+\\-]" "" text)
Edit: With the developmental version of Magit (what will be v2.91.0), you can strip the diff markers by marking a region of a hunk and calling
magit-copy-section-value with a prefix argument.