Can you delete emails from your computer but not server?

My issue is that I have quite a quite a few e-mails on my account, but I use Windows Live Mail and it downloads the e-mails to your computer. Now I know some people will say just delete them and be done with it, but I am one of those people who like to keep such things just in case. I know I'll probably never use them but I still don't want to permanently delete them just in case something happens that I do need them. But at the same time I want to do some cleaning of my computer and e-mails seem to be a good place to do some cleaning. So as the title says, can I delete the e-mails off of my computer without deleting them off of the e-mail server. I figure that I don't care if the server is loaded down, just so long as my computer isn't filled with stuff I don't need. So now the question is can I?