Unfortunately, you cannot do this. For whatever reasons, Apple has not heavily integrated the MPEG formats into Quicktime. Yes, you can play them back, but you CANNOT edit them in any way, shape or form. I believe the only way you can edit MPEG movies on Mac is with Adobe Premier, or EditDV. Both solutions cost several hundred dollars.
Even if you try to cut a short segment from an MPEG clip, Quicktime puts a virtual "wrapper" around that clip. What that does is show you the clip, but it still retains the entire file. Hence, you can never shrink an MPEG movie down using QT.
Note that Apple has also notintegrated MPEG 4.2, or AVI i263 into QT. As advanced as Apple wants you to believe Quicktime is, it's terribly behind in viewing video formats.