Recent single-molecule experiments reveal that mechanical tension on DNA can control both the speed and direction of the DNA polymerase motor. We present a theoretical description of this tension-induced "tuning" and "switching." The internal conformational states of the enzyme motor are represented as nodes, and the allowed transitions between states as links, of a biochemical network. The motor moves along the DNA by cycling through a given sequence of internal states. Tension and other external control parameters, particularly the ambient concentrations of enzyme, nucleotides, and pyrophosphates, couple into the internal conformational dynamics of the motor, thereby regulating the steady-state flux through the network. The network links are specified by bulk-phase kinetic data (in the absence of tension), and rudimentary models are used to describe the dependence on tension of key links. We find that this network analysis simulates well the chief results from single-molecule experiments including the tension-induced attenuation of polymerase activity, the onset of exonucleolysis at high tension, and insensitivity to large changes in concentration of the enzyme. A major dependence of the switching tension on the nucleotide concentration is also predicted.