microwaves are at the wavelength that 'excites' / 'wobbles' / 'resonates' (pick your analogy of ball and spring physics) the O-H bond. H2O is entirely O-H bonds (give or take) and hence microwaves heat food vicariously via the water in it (heating up day old rice from the fridge is easier/better if you put a few mL of water in it). Peroxide peroxide is H-O-O-H so plenty of O-H bonds to excite and hence decompose...
These guy tested the decomposition of hydrogen peroxide across a range of microwave frequencies.
Since hydrogen peroxide decomposes when heated, I'm guessing it's just due to the microwaves heating the mixture.