How do I copy selected faces on a rigged character to a new file? I want to copy to another file selected faces from a mesh.

This has always been a pain and I assume that this is the the only way to do it. 

You CTRL-C the selected object that has the faces you want to move, open a new file, hit CTRL-V, then start removing everything it took with it, such as the skeleton, the unwanted parts of the object, etc. 

Is there a way to just copy faces and paste them on a new file?
Go into Edit mode, select the faces you want to separate
Duplicate the faces, separate them into new object with P
In Object mode select object with the separated faces. Rename it accordingly
Save your file
In a new file execute Append from file, choose the renamed object from the file you saved before