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When I engage the blades PTO, engine bogs down, but keeps running. If I mow, the engine conyiues to bog dowm more until it barely moves & the blades are barely run. The engine does NOT quit running, but I'm loosing power. Once the PTO is dis-engaged, the engine recovers.

The first thing I would check is the deck belts and if the blades are turning freely.

what engine? I've seen the Kohler engines do this and "most" times it is a bad o2 sensor not sending data for more fuel

There is no O2 sensor on this engine that I know of.

If it has an O2 sensor, it is most likely on/in the muffler with one wire coming out.