Is there any way to prevent tmux freezing when lots of text is output to the terminal?

The correct solution is to look at the c0-* options to tmux to try and rate-limit the output. The reason this problem exists at all is due to data being sent to the terminal faster than it can display it, so rate-limiting is the only way.

I still have this problem in tmux 1.6-2 on Ubuntu 12.10. One workaround that I've found is to detatch from the session (prefix+d) and then reattach (tmux attach, good candidate for a quick shell alias). It looks like tmux is actually responsive under the hood---you can confirm that your process is actually killed immediately with ctrl-c---it's just the drawing that's blocking. Detatch works immediately, and when you reattach, the drawing will have skipped to the end.

As far as I know there is no way to prevent it in current releases but some work is ongoing. You can find some patches on tmux's mailing list http://thread.gmane.org/gmane.comp.terminal-emulators.tmux.user/2689.

A good keyword to search the web is "flow control".