Some people believe that a two-edged sword is more dangerous to its user than a single-edged one, but my experience (in martial arts) does not concur. It's not likely that a skilled swordsman is going to hurt himself with the reverse edge.
A two-edged sword is designed to be more dangerous to the target, not the wielder, by cutting on both the forward stroke and the back stroke. This idea is consistent with some of the earlier uses of the phrase:
The burden of taxes, like a two-edged sword, reduced men to poverty, and exposed them to be seduced by bribery. (1809)
In this sense, it is likened to the phrase: "cuts both ways" - referring again to the two sides of the sword stroke.
I don't know at what point "cuts both ways" and "two-edged sword" came to have the current meaning of good and bad, instead of just bad and worse, but I expect the two phrases evolved together.