We show that a mesoscale model, with a minimal number of parameters, can well describe the thermomechanical and mechanochemical behavior of homogeneous DNA at thermal equilibrium under tension and torque. We predict critical temperatures for denaturation under torque and stretch, phase diagrams for stable DNA, probe/response profiles under mechanical loads, and the density of dsDNA as a function of stretch and twist. We compare our predictions with available single molecule manipulation experiments and find strong agreement. In particular we elucidate the difference between angularly constrained and unconstrained overstretching. We propose that the smoothness of the angularly constrained overstretching transition is a consequence of the molecule being in the vicinity of criticality for a broad range of values of applied tension.