Just to get this out of the way... your video and audio aren't on separate layers, are they?
No they aren't.
I would highly recommend you do not try to edit a video in After Effects. After Effects is not made to edit videos. Edit your videos in Adobe Premiere Pro.
If you want to use After Effects to do advanced color grading, add motion graphics, do advanced compositing, or add visual effects, you can easily import your Premiere Pro Project into AE.
If, however, you are determined to do it in AE, please describe your project and workflow more clearly. For example, what do you mean by "cutting" your video? There is no cut command in AE.