You appear to have an open contour profile for your revolve. I can't be sure but did you make a revolve surface instead of a revolve Boss/Base?
EDIT: Just double checked what forum I am in. Instead of using an Extrude Cut use the Surface Trim command and you will be able to cut the hole out of the surface.
Also, you could incorporate the hole you are attempting to make into the original sketch's profile and make it in a single feature. You might do that as well.
Per SOLIDWORKS Solution Id: S-055798, Surfaces cannot be cut by Solid Body features such as a Cut-Extrude.
Thank you for your input. I see it was because I was using a surface.
Thank you, Ryan.
I did use a revolve surface instead of a revolve boss/base. Once I converted to a revolve boss/base, I as able to cut. I now understand the issue was using a zero-thickness 'surface', which cannot be cut.
Thank you for your input, it helped me understand, and solve, my situation.