How to cut this shape

There is no need to be very precise with this, because you could just hide in below the figure. So with the pentool you roughly draw a line (and really: just make corner points) that leaves room for adjusting the layout. Close that shape by continuing it so that it fully covers up the botto left of the circle. Fill it with black.

Then you can create an opacity mask.

https://helpx.adobe.com/in/illustrator/how-to/illustrator-opacity-masks-transparency.html