You can get that "cross section" of the circle. This logo wouldn't be that hard to do actually. The only trouble you may encounter is what you expect from the "quality" or rendering style of the 3D extrusion. Anime Studio is not a dedicated 3D application, so there aren't a lot of options for that type of 3D effect.
The trick is to figure out where the cross section cutaways are on the circle, and "split" the curve of the circle so you get enough points to maintain the shape and also to add in the cross cutaway sections.
What I do when I need this type of thing, is to use the script "Draw/Split Curve..." Using that script under the Scripts menu, will give you the option to choose how many points to split or "add" evenly to the circle. This will add points without distortion. It evenly distributes the points around the circle. The good part is that you can easily rotate the points to line up with the cross section with very minimal distortion of the circle.
For example you could add points evenly to the circle then select matching opposite points and simply rotate around to line up with where you want the cross sections to "cut away". You would then just add in the cross sections across those points of the circle and only fill the sections you need.
Moving the extra points you added to the circle won't distort it very much at all even if they aren't perfectly evenly spaced out around the circle.
I did this sample in just a few minutes:
