There are two approaches.
One is to use something like Handbrake to convert the DVD to an editable movie on your hard drive. Then you can extract the clip you like.
The other is to get SnapZ Pro which lets you make screen captures at video rates. Play the DVD at the smallest size possible that has the resolution you need. In other words, don't expand it to full screen. Play it at normal size or smaller if you don't need that resolution. Then with SnapZ Pro set a window around that area. Play the movie and capture that part of the screen at the desired frame rate. Works well.