Get the free trial of VideoReDo TV Suite. Set it up to save your cuts rather than delete them…in other words, use the Scene mode instead of the Cut mode.
The trial for VideoReDo TV Suite is fully functional, and will not put any type of watermark on your video. Nor is there a size limit for the video you will be working with.
A completely free program that can do this same sort of thing (though far less versatile for working with the mpg2 found in dvd video) is AviDemux. It will only work in cut mode, so you have to cut around what you want left. Use copy for audio and video, and set the output format to mpeg ts, and make certain to use a .mpg file extension on the output file.
Edit: And DVDShrink will work also as cholla pointed out. If you want mpeg instead of a small dvd-video, you could rename the vob file to use an mpeg extension, or run the small dvd video through Vob2Mpeg