Characterization of energy landscape of metalloproteins is challenging because of the subtle changes imparted by metal binding on the stability and conformational flexibility of proteins. Here we present copper-binding induced changes in the mechanical unfolding pathways of azurin, a β-barrel protein with type-I copper center, through a joint experimental-computational study. Single-molecule force spectroscopy experiments reveal an intermediate along the unfolding pathway of apo-azurin in half of population. Steered molecular dynamics simulations attribute the native and intermediate unfolding transition states (TSs) to the rupture of interactions between the pairs of β-strands, 2B-8 and 4-7, respectively. We show that the copper-binding does not change the first TS of azurin and its mechanical properties, but influences the second TS. The rupture of 4-7 β-strand pair is delayed in holo-azurin because of constraints imposed by the copper coordination sphere and occurs after the second TS. Our experimental and computational approach extracts unprecedented details along the unfolding landscape for apo- and holo- forms of azurin.