How can I get rid of the mission voice-overs?

Solution 1:

Turning down the voice volume will stop all voice acting everywhere, but I don't think that there's another way. The voice acting in mission descriptions is almost always the exact same as the text, and they usually only read the first paragraph or so anyway.

You can also turn on subtitles for the radio and election speeches, but I don't think that anything important is in those since you can turn them off in the options. The radio is usually just jokes about recent happenings, and the election speeches are pretty much just speeches.

Solution 2:

Maybe you can use a .hpk archiver (http://www.techpowerup.com/forums/showthread.php?t=113705 might work) and remove/replace the voice files in Tropico 4\Local\voice\English.hpk. Don't forget to make a backup.