Why does decrease in dislocation density result in higher ductility?

Dislocations travel through a metal crystal while it is being deformed; it is in fact dislocation movement which makes metal crystals yield and deform at loads far below that which you could calculate on the basis of interatomic forces in a perfect lattice.

These mobile dislocations tend to pile up against one another and become entangled as the material deforms; these pileups inhibit further deformation and the material becomes more resistant to deformation than it was originally. This furnishes the basis for cold work as a strengthening mechanism.

If there are not many dislocations in the crystal to start with, then those which are present find it easy to move, and it is easy to form new ones from things like stacking faults within the crystal. This makes the crystal ductile- at least until dislocation pileup sets in.