You can break a contour at any node. When you break a closed path or contour, you open it. When you break an open path or contour, you create two separate contours.
There are two ways to break contours: at a node or with the Pen tool.
To break a contour at a node:
From the Tools toolbar, select
the Pen tool 
.
From the Tool Options palette,
select the Edit Mode 
.
Select the node you want to break the contour at.
Do one of the following:
Choose Objects > Edit > Break (Ctrl+K).
Right-click the node and choose Edit > Break from the context menu.
The path or contour breaks and a new node is added on top of the current node. The node square changes to a node-on-node indicator. Drag one node away to separate them.
To break a contour with the Pen tool:
From the Tools toolbar, select
the Pen tool 
.
From the Tool Options palette,
select the Knife Mode 
.
Select the contour you want to break.
Click and drag across the contour where you want it to break.
Note: The Knife Mode of the Pen tool will cut through all selected contours in an object.
Adding or Removing Nodes on a Contour
Reversing the Direction of Contours or Paths