How to cut a shape in 3D object?

As explained previously, the limited feature set of 3D Effect does not let you contain different-length extrusions or differently-oriented extrusions in a single model.

Essentially, what you are wanting to do is contain the two identical extruded cross-sections in a single 3D model space, aligned concentrically in the extrusion direction (that much is possible), but with one more distant from the origin in the direction of the extrusion (that part is not possible).

If you wanted your final rendering to be parallel perspective (set the perspective slider set all the way to zero), it would be trivial to just use two separate models:

But since your screenshot implies you want to end up a converging perspective, it would be tedious to get the perspective settings of two separate models to appear to align.

In Illustrator's 3D Effect, the shape of the sides of an extrusion is determined by shape of the Bevel profile. You can create additional Bevel profiles by [the tedious process of] opening the Bevels.ai file, drawing the profile, storing it as a Symbol in that document, saving that document, quitting and re-launching Illustrator.

A Bevel profile can have multiple "bumps":

If you apply a profile like those shown above using the outer bevel option, and scale the base path to a very small size, then the result will look like a row of separate extruded objects, connected by a thin "thread" through their centers. If the model is oriented so as to hide the "thread", it looks like what you are trying to do. Because your posted example is slender, the orientation you desire may not hide the "thread." But it would be fairly trivial to manually delete the paths which constitute the "thread" after expanding the Effect.

However, there's no reason why you can't combine the converging perspective generated by 3D Effect with ordinary 2D perspective techniques on the page:

JET

Depends on what you mean.

Assuming that is a 3D Effect object, then it is an extrusion. As long as the Effect is "live", any changes you make to the 2D base path will update the 3D extrusion. So you can make changes to the face of the object, because that is the shape being extruded. For example, you can create a hole in the face of the object by making it a Compound Path. The inner subpath(s) of the Compound Path will become Bolean subtractions in the direction of the extrusion.

But you cannot, for example, cut a hole through the sides of the extrusion because that is not derived from the base path, and because the limited feature set of 3D Effect does not let you contain different length extrusions or differently-oriented extrusions or different kinds of 3D transformations (e.g., a revolve object and an extrusion object) in the same 3D coordinate system (model).

JET

No, Illustrator cannot do 3D boolean operations.

What you can do is map artwork to the 3D shape. Then expand the appearance and use the mapped artwork as a guide for further path editing.