cut one path from the other

hendy,

Depending on requirements, you can simply mask out parts (of the black) in a simple way with an Opacity Mask; the word look in "so the black looks cut out?" seems to imply that it is sufficient; and it is reversible and editable.

You can:

1) Place the mask out path(s) as desired, and Group them if there are more than one, and give it/them a black fill and no stroke;

2) Select (only) the mask out path(s) and the (black) path to be masked out from and tick Make (Opacity) Mask in the Transparency palette.