The git-archive command will do almost what you want, but it should work with an already cloned repo, therefore, you have SSH access to the host, you can do:
cd /path/to/destination ssh user@host "cd /path/to/repo && git archive HEAD dir/you/want" | tar xf -
Or with compression for network transport:
cd /path/to/destination ssh user@host "cd /path/to/repo && git archive HEAD dir/you/want | gzip" | tar xzf -
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