After you scan the disc, you hit the Re-Author button.
Now, let's say you want to cut out chapter 5. You need to drag/drop two copies of the movie from the right column to the left.
Select the first copy, and press "Set Start-End frames". Set the top slider over to the beginning of the film, and the slider below it to the end point - in this case, the end of chapter 4 (you can select chapters from the drop down list.)
Now, select the second copy, and this time, set the top slide to the beginning of chapter 6, and the slider below it to the end of the film. Then press Backup! and select a directory.
When it's done, you will have several files. What you need to find are the two VOBs. One VOB will be from the beginning of the film to Chpt 4, and the other from be from Chpt 6 to the end of the film. There are a variety of MPEG joining utilities that can merge the two files into one film. (If the segments are very long, you may have a VOB over 2Gbs. This can be a problem if you are not using NTFS.)