Hydrogen peroxide is widely used as a DIY treatment to kill mold. It's a strong oxidizer and is listed as a popular mold treatment by the U.S. Department of Housing and Urban Development. It's not known which, if any, species of mold are resistant to hydrogen peroxide.
Hydrogen peroxide's disinfecting properties come from its reactivity. The chemical formula for hydrogen peroxide is H2O2. The two oxygen atoms readily bond with and split other molecules. For biological entities such as mold, this means their surface layers are attacked, which leads to more oxygen attacking the inside of the organism and eventual death.
Humans can experience similar effects if concentrations of hydrogen peroxide are high enough. Even solutions of 3 percent hydrogen peroxide are corrosive to humans. Most household solutions of hydrogen peroxide are very dilute, yet they're still effective at killing fungus and bacteria. Molds are a variety of fungus, and general antifungal treatments should also be effective against them.