The cutting tools tutorial

• The Crop tool: draws a rectangle through objects, everything outside the rectangle is then deleted. Works for simple objects, complex objects are converted to a bitmap, after which the bitmap is cropped.

• The Knife tool: useful tool, click on one side of an object, next click on the other side of the object, and the object will be cut into two by a straight line between the two points. Cutting along a curved line can be done by keeping the mouse button pressed while moving from side to side. It is important to watch the mouse cursor during operation, the tool only works you click when the cursor knife symbol points straight down. After cutting the two halves can be selected separately.

• The Eraser tool: similar to the knife tool, but cuts with a thick zone, and this tool only works when it is dragged. Another difference is that the resulting object, although consisting of two halves, still is a single object. To separate the two halves you need to break the object apart: arrange > Break apart (ctrl K)
  
• Virtual Segment Delete tool: deletes parts of an object behind crossed lines. It's best explained by the image below:

Source : http://personal.strath.ac.uk/yannick.kremer/Corel/Cutting.html