rsync delete files from target if not existing in source

Yes, --delete and --ignore-existing options of rsync will work together.

Here is a test (check the modification times especially):

:~/foo$ ls -l
-rw-rw-r-- 1 user user 0 Mar 27 14:38 egg.txt
-rw-rw-r-- 1 user user 0 Mar 27 14:38 ignore.txt
-rw-rw-r-- 1 user user 0 Mar 27 14:38 spam.txt

:~/bar$ ls -l
-rw-rw-r-- 1 user user 0 Mar 27 14:40 ignore.txt
-rw-rw-r-- 1 user user 0 Mar 27 14:40 remove.txt

$ rsync -r --delete --ignore-existing ~/foo/ ~/bar/

:~/bar$ ls -l
-rw-rw-r-- 1 user user 0 Mar 27 14:42 egg.txt
-rw-rw-r-- 1 user user 0 Mar 27 14:40 ignore.txt
-rw-rw-r-- 1 user user 0 Mar 27 14:42 spam.txt

This works only partially

From rsync man page:

[..]
--delete                delete extraneous files from dest dirs
[..]
--ignore-existing       skip updating files that exist on receiver
[..]

Example:

% ls ~/tmp/A       
123  456
% ls ~/tmp/B
456

% rsync --recursive --ignore-existing --delete ~/tmp/A/ ~/tmp/B
% ls ~/tmp/B                                                   
123  456

% rm ~/tmp/A/456

% rsync --recursive --ignore-existing --delete ~/tmp/A/ ~/tmp/B
% ls ~/tmp/B                                                   
123

% touch ~/tmp/B/789
% ls ~/tmp/B       
123  789

% rsync --recursive --ignore-existing --delete ~/tmp/A/ ~/tmp/B
% ls ~/tmp/B                                                   
123

Now pay attention to the change date of 456

% ls -la ~/tmp/A
insgesamt 8
drwxrwxr-x 2 aboettger aboettger 4096 Mär 27 09:41 .
drwxrwxr-x 7 aboettger aboettger 4096 Mär 27 09:25 ..
-rw-rw-r-- 1 aboettger aboettger    0 Mär 27 09:35 123
-rw-rw-r-- 1 aboettger aboettger    0 Mär 27 09:42 456

% rsync --recursive --ignore-existing --delete ~/tmp/A/ ~/tmp/B

% ls -la ~/tmp/B                                               
insgesamt 8
drwxrwxr-x 2 aboettger aboettger 4096 Mär 27 09:45 .
drwxrwxr-x 7 aboettger aboettger 4096 Mär 27 09:25 ..
-rw-rw-r-- 1 aboettger aboettger    0 Mär 27 09:35 123
-rw-rw-r-- 1 aboettger aboettger    0 Mär 27 09:42 456

% touch ~/tmp/A/456

% ls -la ~/tmp/A   
insgesamt 8
drwxrwxr-x 2 aboettger aboettger 4096 Mär 27 09:41 .
drwxrwxr-x 7 aboettger aboettger 4096 Mär 27 09:25 ..
-rw-rw-r-- 1 aboettger aboettger    0 Mär 27 09:35 123
-rw-rw-r-- 1 aboettger aboettger    0 Mär 27 09:46 456

% rsync --recursive --ignore-existing --delete ~/tmp/A/ ~/tmp/B

% ls -la ~/tmp/B                                               
insgesamt 8
drwxrwxr-x 2 aboettger aboettger 4096 Mär 27 09:45 .
drwxrwxr-x 7 aboettger aboettger 4096 Mär 27 09:25 ..
-rw-rw-r-- 1 aboettger aboettger    0 Mär 27 09:35 123
-rw-rw-r-- 1 aboettger aboettger    0 Mär 27 09:42 456