Why are oxyacids strong oxidizing agents?
Your premise is incorrect. Some oxyacids are oxidising agents. Some are not. Take e.g. carbonic acid. You cannot oxidise anything with carbonic acid, really.

Also, the choice of words is bad. Sulphurous acid (or hydrogen sulphonic acid; it doesn’t really make a difference; both are structural isomers) is also an oxyacid ($\ce{H2SO3}$) however it is a pretty good reducing agent oxidising itself to sulphuric acid. Heck, technically $\ce{H4SiO4}$ is an oxyacid, too, but it won’t oxidise anything at all.

So reducing the question to where it is correct we arrive at:


  Why are some oxyacids where the central atom is in its highest possible oxidation state strong oxidising agents?


And it basically answers itself. Depending on the electronegativity of the central atom it will be more or less ‘happy’ to cede all its valence electrons to oxygens and be the centre of an oxyacid. For those that don’t like that lot in life, most notably nitric acid, they will often find species whose electrons they can take back (the atoms are electronegative after all) and thus oxidise them.