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[Rick Gerard]

Turn off the eyeball on a video layer and you turn off the video. Turn off the speaker icon and you turn of the sound. Both are in the timeline. They are right next to each other.

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[P.M.B]

What do you mean "separate"?     You mean how do get yourself an independant audio file like an mp3 or aiff with no video?   Just render it out to an audio only format.  And logically the opposite is also true.  Re-render the video to a lossless format with the audio option turned off.  We could give you better information of you tell us specifically what your end goal is, WHY you want to "separate" it.  Example: Do you need to deliver a video file with no audio.  Or are you trying to use the audio in another project and want to keep the file size small?   

[Mylenium]

Yes, technically an actual separation an only be done in Premiere. Audio is a property of the A/V layer and unless it is already an audio-only type, there is no way to unglue it from the video in AE. As suggested, you would work with a duplicate layer with the video disabled and on the other you would turn off the audio.

Mylenium

[ShiveringCactus]

Adding this to illustrate Mylenium's point:

It really boils down to how AE and PP present the audio.  In Premiere Pro, you see the audio tracks separately, but moving the audio also moves the video (unless you break the link).  In After Effects, once you duplicate the layers, there is no link between them (although you can use markers to visually line them up and I suppose you could also use Time Remapping to link them, but I'm not sure why you'd want to)