Can SimplePie generate new feeds?

Sort of.

Is there a way to hack together a new feed from SimplePie data? Yes. See http://simplepie.org/support/viewtopic.php?id=1068

Is there a clean, programmatic way of generating new feeds? Not yet. In SimplePie 2.0, we're planning to move to PHP's DOM extension, which will make things like this very easy with very little overhead. Until then, SimplePie will continue to strive to be the best way to manage the reading of feeds in PHP.