how to cut selection to new layer in after effects?

You're working in Krita, right?  Save the file as a PSD and you can import that as a Comp in AE.  Or, you can save the file as a PNG with transparency or a TIFF with transparency and import that as Source Footage into AE.

PSD, PNG or TIFF will allow you to layer your artwork over other layers in AE as a background.

The Krita online User Manual discusses file formats under File Formats > Openness.

-Warren

As imeilfx say's you can do it as track matte function, also if you want to play with shapes layer you can do it directly inside your shape layer using merge option, check this quick demo

I'm not sure that I understood you correctly but I guess the thing you looking for are mattes (track matte function). If that is the case - most of how to do that you will find here: Use alpha channels, masks, and mattes in After Effects