MPEG StreamClip can definitely edit out selections and it does it quite well as a matter of fact. Selecting sections to remove is NOT very intuitive however, until you know the secret. Once you do, it makes perfect sense.
Here's how to mark and cut selection:
1. Advance frames until you get to the start of the advertisement.
2. Use the I key to mark the start of the selection. (in MPEG StreamClip the I key stands for for IN)
3. Advance to the end of the advertisement and then hit the O key (for Out)
4. Use CMD-X to cut the selection.
5. Repeat from Step 1 as needed.
Enjoy!