The best way to achieve this is to create a segment for folks that clicked on the specific link and then exclude that segment from the "Review and Send" page. To do this head over to the response overview of the original mailing, click on the "Clicks" tab, select the specific link, then use the "Save this tab as a segment" button at the top right of the list.
This is going to create a segment in your account for everyone that clicked that link. When you go to resend the mailing, on the Review and Send screen you'll see a checkbox "Exclude segment" and when checked you'll be given a drop-down menu of segments in your account, go ahead and select the segment you just created and they'll be excluded from that send.
That should do the trick! Let me know if you have any questions :)