For fuck's sake, what's so hard to get your head around???

The spaceshuttle doesn't 'leave anything behind', nor does your average fireworks rocket.

As Nige explained, very clearly might I add, the shell contains both propellant and warhead.
The shell is nothing more than a stabilized tube filled with a fuel and a warhead on top.
When the fuel ignites (by means of the fixed firing pin) it burns so rapidly that it propelles the shell out of the mortar tube.