Why do tensile testing graphs show a negative slope at these regions?
It's an issue of lateral contraction and whether or not it is being considered.
As OldEngr63 states, engineering stress vs. strain is just a scaled version of force vs. deformation. Either way, you'd get a plot that looks like the one the TS posted.
As I said before, however, true stress vs. strain would NOT look like the plot that the TS posted.