Can cutting pressure treated wood harm my saw blade?
You have to cut the wood somehow... You can give your blades a wipedown with a slightly damp rag to remove sawdust particles (let them air-dry well afterward), but I wouldn't worry too much. 

Corrosion involving PT lumber is mostly a problem with long-term contact; the copper compounds in the chemical treatment are more "galvanically noble" than many common metals including carbon steel, and so an electrochemical reaction will result in the less noble metal (here the steel or iron) oxidizing. The same happens with ordinary zinc-coated or uncoated iron or steel fasteners in PT construction. To prevent this, stainless steel alloys (containing low carbon and higher concentrations of even nobler metals like chrome and nickel) or hot-dip galvanized fasteners (which cover the steel with a thick protective coating of zinc oxide which shields the fastener against further corrosion), are recommended for long-term contact with pressure-treated wood (on the scale of years). 

However, your carbon-steel/carbide saw blade will only be in contact with the wood and its chemicals for some seconds. Your saw blades will dull naturally through age and use before the chemicals have any detectable effect.