One problem with doing that is the level of signal from that output. It might be too hot to go straight into a mixer or some other line level device...though if you keep the master low enough it might work. But even then, you're going to need some pretty heavy EQ to get a decent sound...though some have had decent results running it into something like a POD, bypassing the preamp and just using the speaker cab sims...you could also add an EQ pedal somewhere in there...but it's a lot of work if you can mic easily enough.
One more thing to try would be the Behringer Ultra-G DI...goes between the amp and speaker and has an XLR line out with an optional 4x12 cab voicing switch. I've not tried one myself, but have heard some things recorded that way that sounded pretty good...and the users seem to like them. They're only like $35, so you don't have much to loose by trying one. Of course, your speaker is still hooked up, so it's not a solution for silent recording.