I can't help with how to do it in Carrara, cause I never modelled with it, just a bit of vert. tweeking is all; but...
The Max slice modifier is either:
a) cutting a face(s) into 2 parts, or
b) cutting an object into 2 parts.
The cut is done by a plane that can be moved around as needed.
At least when a carrara modeller comes along here to answer the question (I'm sure there will be a way to do it w/ Carrara), they won't have to ask what the Slice does in Max.

---

Silo might be 'only a modeller'; but it is a damn good modeller. I don't use that either by the way, just going by what people in the 3d modelling forum here say.
I'd imagine a 3ds max tute isn't easy to follow in Carrara, since there likely a lot of procedures that Max does that aren't done the same way in Carrara. Not saying that Carrara can't maybe do them, it would just do them in a different way.

Friends don't let friends use booleans.