How do I stop the toolpath cutting past the edge of my 3D model?

Aspire and VCarve V8.0 and Higher.

Modelmachininglimit

A new feature of Aspire and VCarve, is the option to automatically limit a 3D toolpath to the model boundary.

Just select this option when setting up your 3D toolpathing.

Aspire v4.5 and Lower.

If you select a closed vector shape before calculating the 3D Roughing and 3D Finish toolpaths, the toolpaths will observe the vector as a machining boundary and stay inside of it. Without this, the toolpaths will calculate for the entire surface of the material which can add significantly to the machining time.

There are a couple of ways to create this machining boundary vector. It may be as easy as creating a vector shape with the drawing tools (circle, ellipse, rectangle, etc.) or you may want a vector that follows the exact profile of the 3D model. In this case, you can use the Create vector boundary from selected components tool   found in the Modeling Tools on the Modeling tab OR use the Fit vectors to bitmap tool  found on the Drawing tab. 

Once the boundary vector has been created, the 3D Roughing and Finishing toolpaths include a setting called Boundary Vector Offset, which can be adjusted to allow the toolpaths to extend past the boundary by the set amount or have them short of the boundary by the set amount.