I know how to remove partial scenes from the timeline events, but how do I permanently remove a portion of the original clip? I have some blurry stuff that I will never use and want to permanently remove it.
Well, you can always choose to capture only the part of the video you want to use...
Otherwise, the only way to permanently change the saved clip (as opposed to the event you've added to the timeline) is to create a file in Screenblast, add the clip to your timeline, trim off what you don't want and then export it as a new, cleaned-up AVI. (You can throw away the old one.)