If you have a Standard or Advanced license you alternatively can use the Split Polygons tool on the Advanced Editing toolbar to split polygons with existing line features during an edit session.
If you have an Advanced License you can use the Features to Polygon tool in a geoprocessing workflow.
Another way to do this (which I can't seem to find anywhere in the documentation) is to use the Cut Polygons Tool. After you select the polygon you want to cut, right click on a feature that completely crosses the polgyon and select Replace Sketch.
You'll then have the feature highlighted
If you're satisfied, hit the F2 button (Finish Sketch) which clips the selected polygon with your feature
The Replace Sketch behavior definitely needs to be better documented. The only mention I found in the help is a Tip in the middle of this help topic that vaguely describes what the Replace Sketch Editor menu option does. I guess that is why the Forums and Geonet exist, so we can get help from those who know what actually works in the real world.
It seems pretty simple and I assume it can be done at any license level. Does it preserve the attributes of the original polygon? I came across another post that suggested that it might not.
(Edit: Sorry Ken for originally attributing your post to Dan. Dan Patterson has jumped in on so many discussions I have followed lately that I just glanced over the name and when I saw the first name was 3 letters long I assumed it came from him).