You have the visitors that you do for a reason, changing everything will lose some of those visitors. If your site hasn't been steadily increasing in both new visitors and increasing in duration for return visits you will need to rely on your new design to convince those people to change their ways, to attract more hits from the search engines, encourage people to spread by word of mouth (including blogging) how great your site is, and to spend more time themselves on each visit - a tall order.
Rather than dump everything, assuming that the previous content was any good, keep the prior content on the Previous Issues webpage, as is done on these sites:
See how each of those websites lays out the current edition on the webpage, but if one wanted to read prior issues it's still available. That way you don't lose current traffic or readers, present a fresh style that might attract new readership, and appear more organized and accessable. That puts your history hidden under one link, a click away, and once in there the Main page is also a click away.
It's barely a couple of hours work to type out the archive list and simple enough to automate. Your magazine will have a fresh start without throwing out it's history. If you really hate the old content you can make the 'Prior Issues' link harder to find.
All the keywords on those old webpages are a link to a hit from a search engine, removing all your pages will invalidate all searches - an annoyance to someone whom thought they found what they wanted, now they are redirected and need to know (and must rely on) your search bar to find what they are looking for - but you've deleted it!
If you find months from now that the old content is unwanted it's easy to adjust the 'Prior Issues' webpage to cut off a few months back. You can always delete it later, bringing it back after removal is the tricky part.
It is only if it's the case that your old content is extremely poor that you would want to delete it, in that case you'll need to convince new users that you've changed your ways and convince your fans that they will enjoy the better content.
If your site doesn't have a bad rep, and is continuing on the same subject, keeping the domain name makes sense; as does keeping the search engine's links to those pages. It's easy for people to 'get out of there' by hitting the [Home] button in the upper left, everyone knows that, and when they do they'll be treated to your fresh new style.
See also: List of Online Magazines