How can a mineral display both cleavage and fracture?
It can display both.
Cleavage is a growth plane in the mineral, due to the structure of atoms. This means the cleavage is an easy plane to 'cleave-along', meaning the mineral prefers to break along this plane.
A fracture can happen in any direction, but usually a fracture will happen if it more energetically favourable. If the crystal grew with a dislocation in the lattice, this may act a weak point, so a fracture could occur along it.
So cleavage is characteristic to the mineral (based on the structure) and a fracture can happen independent of the mineral's atomic structure.