A green curve is a dependent curve. It's very important to understand sub-object dependencies when trimming in MAX. The Vector Projected Curve (the surface curve) is dependent on the curve from which it was projected. If we move the curve, or any of its CVs, the surface curve will update as if it were reprojected from the edited curve.

The Vector Projected Curve is equally dependent on the surface. If the shape of the surface is changed, the surface curve will update as if it were reprojected on the edited surface.

Now we're ready for the second step. We can trim by removing everything inside the surface curve.

Or we can remove everything outside of the curve.

Let's understand precisely what happened when the surface was trimmed. The original surface is structurally unaffected by the trim. For example, if it's an independent surface with its own CVs, all of the CVs are still present, regardless of whether they are inside or outside the trim curve.

Editing the surface CVs simply modifies the surface prior to the application of the trim curve, allowing you to work on a surface with the trim already on.

For those of you who haven't seen MAX 3 yet—I'm using the Pre-Release version here--the axis device in the last image is the new Transform Gizmo. This is a much loved feature of MAYA that MAX has adopted, allowing you to move, rotate and scale in a given direction by dragging on the appropriate handle. This makes life much easier.