We investigate electron and phonon transport through defected graphene nanoribbons (GNRs). For phonon transport, we develop an efficient linear scaling method which is based on the Chebyshev polynomial expansion of the time evolution operator and the Lanczos tridiagonalization scheme, and also use molecular dynamics simulations. We show that edge-defects reduce phonon thermal transport dramatically in both armchair and zigzag GNRs, while in zigzag GNRs edge-defects are only weakly detrimental to electronic conduction. On the other hand, bulk defects suppress both charge and thermal transport for relatively high density of defects. The behavior of the electronic and phononic elastic mean free paths of zigzag GNRs with edge-defects points to the possibility of realizing an electron-crystal coexisting with a phonon-glass.