Single-molecule mechanical experiments have proven to be ideal tools for probing the energetics and mechanics of large proteins and domains. In this paper, we investigate the nucleotide-dependent unfolding mechanics of the nucleotide-binding domain (NBD) of the Hsp70 chaperone DnaK. The NBD binds ADP or ATP in the binding cleft formed by lobe I and lobe II, which consists of two subdomains each. When force is applied to the termini of the NBD, the observed unfolding forces are independent of the nucleotide state. In contrast, when force is applied across the nucleotide-binding pocket, the unfolding forces report specifically on the nucleotide-phosphate state. In this active, ligand-responsive pulling geometry, we observed a bifurcation of the unfolding pathway; the pathway proceeds either through a cooperative "coupled pathway" or through a noncooperative "uncoupled pathway". The partitioning between individual unfolding pathways can be effectively tuned by mutation or by the nucleotide exchange factor GrpE, i.e., by the factors affecting the strength of the lobe I-lobe II interactions within the native NBD. These experiments provide important insight into the molecular origin of the internal signaling between the subdomains of the nucleotide-binding domain of Hsp70 proteins and how signals are efficiently transferred inside the protein molecule.